0
Add your answer:
Earn +20 pts
What are the steps in finding the common monomial factor?
It is similar to finding the greatest common factor only you may have variables involved, so you may factor a constant and variable(s) which all terms are divisible by, for example: The common monomial factor in the following: 5x^2+5x would be 5x because both terms are divisible by 5 and x. 5x (x+1). Just find the constant and variable all terms are divisible by and then the product of those is your common monomial factor.
What is the trick to finding the greatest common factor?
The following answer describes four methods of finding the greatest common factor, with examples, and several "tricks" or shortcuts that can make it easier.Method: Guess and RefineSometimes, you can look at two numbers and make a good guess that you can refine.Example 1: Find the greatest common factor of 45 and 50.Because both numbers end in either a 5 or 0, you know that they are both divisible by 5. If you divide both numbers by 5 and the results have no common factors (except 1), 5 is the greatest common factor.45 ÷ 5 = 950 ÷ 5 = 10Since 9 and 10 are consecutive numbers, they have no common factors. Therefore, the greatest common factor is 5.Example 2: Find the greatest common factor of 150 and 750.Both numbers end in 50, so they are both divisible by 50. If you divide both numbers by 50 and the results have another common factor, you continue identifying common factors until you have a pair without common factors.150 ÷ 50 = 3750 ÷ 50 = 15Since 15 is divisible by 3, and 3 is divisible by 3, you have another common factor, which is 3. Then, you can divide the most recent results by 3.3 ÷ 3 = 115 ÷ 3 = 5Since 1 and 5 do not have any common factors, take the two factors that you did identify, 50 and 3, and multiply them together: 50 x 3 = 150. This number, 150, is the greatest common factor.Method: Find All the FactorsIf the numbers are small enough or you know that they have only a few factors, you can list all the factors of each number and compare to determine the largest factor they have in common. One of the related questions links will take you to a page with the complete list of factors for numbers 1 through 100.Example: Find the greatest common factor of 15 and 18.The factors of 15 are 1, 3, 5, and 15.The factors of 18 are 1, 2, 3, 6, 9, and 18.The common factors are 1 and 3, so the greatest common factor is 3.Example: Find the greatest common factor of 26 and 91.The factors of 26 are 1, 2, 13, and 26.The factors of 91 are 1, 7, 13, and 91.The common factors are 1 and 13, so the greatest common factor is 13.Method: Find the Prime FactorsIn situations where you cannot get a good start simply by looking at the numbers, follow the following steps:1. Determine the prime factors of each number. See the related question "How do you find prime factors" for a method on doing this. Also, one of the related questions links will take you to a page with the complete list of prime factors for numbers 1 through 100.2. Determine the prime factors they have in common.3. Multiply all the prime factors they have in common to calculate the greatest common factor. Example: Find the greatest common factor of 5,544 and 37,620.The prime factors of 5,544 are 2, 2, 2, 3, 3, 7, and 11.The prime factors of 37,620 are 2, 2, 3, 3, 5, 11, and 19.The common prime factors are 2, 2, 3, 3, and 11.Therefore, the greatest common factor is 2 x 2 x 3 x 3 x 11 = 396. Example: Find the greatest common factor of 7,888 and 10,002.The prime factors of 7,888 are 2, 2, 2, 2, 17, and 29.The prime factors of 10,002 are 2, 3, and 1667.The common prime factors are a single 2.Therefore, the greatest common factor is 2. Method: Euclidean AlgorithmThis method is more efficient than finding the prime factors when the numbers are large, but teachers might prefer that you gain experience determining the prime factors of numbers. For this method, divide the larger number by the smaller number, then divide the "divisor" from the previous division by the remainder from the previous division, and continue until a number divides evenly. That divisor is the greatest common factor. Example: Find the greatest common factor of 33 and 77.77 ÷ 33 = 2 remainder 1133 ÷ 11 = 3 with no remainderSo, the final divisor, 11, is the greatest common factor. Example: Find the greatest common factor of 27 and 168.168 ÷ 27 = 6 remainder 627 ÷ 6 = 4 remainder 36 ÷ 3 = 2 with no remainderSo, the final divisor, 3, is the greatest common factor.---- Shortcut 1: If one number is a multiple of the other, the smaller number is the greatest common factor, because it is the largest possible factor of itself.Example: Find the greatest common factor of 72 and 288.288 is divisible by 72, therefore 72 is the greatest common factor.Shortcut 2: The greatest common factor of two numbers cannot be larger than the difference between the two numbers. So, you only need to test the numbers that are equal to or less than the difference between those two numbers. Also, the greatest common factor must be a factor of the difference between the two numbers. (This shortcut can help with finding the greatest common factor of three or more numbers. Examples are shown in the related question on finding the greatest common factor of three or more numbers.)Example: Find the greatest common factor of 56 and 64.The difference between 56 and 64 is 64 - 56 = 8. The largest possible common factor is the difference itself. So, check whether 8 divides evenly into both of them.56 ÷ 8 = 764 ÷ 8 = 8Therefore, 8 is the greatest common factor. Example: Find the greatest common factor of 72 and 88.The difference between 88 and 72 is 88 - 72 = 16. Check whether 16 divides evenly into both of them. It does not. But, the greatest common factor must be a factor of 16. The factors of 16 are 1, 2, 4, 8, and 16. So, try the next largest factor, 8, and see if it divides evenly into both of them.72 ÷ 8 = 988 ÷ 8 = 11Therefore, 8 is the greatest common factor.Example: Find the greatest common factor of 1003 and 1180.The difference between 1180 and 1003 is 177. Check whether 177 divides evenly into both of them. It does not. But, the greatest common factor must be a factor of 177. By using the divisibility rule for 3, you know that 3 is a factor of 177, but the divisibility rule indicates that neither 1003 nor 1180 are divisible by 3. 177 ÷ 3 = 59, so check 59 as a factor of both numbers. Note that 3 and 59 are both prime numbers, so they are the only prime factors of 177, so if there is a greatest common factor of 1003 and 1180 other than 1, since we have ruled out 177 and 3, it must be 59.1003 ÷ 59 = 171180 ÷ 59 = 20Therefore, 59 is the greatest common factor. Corollary 1 to Shortcut 2: If the numbers are only one number apart, they are relatively prime and have no common factor other than 1. Example: Find the greatest common factor of 4 and 5.The difference is 1, so the greatest common factor is 1. They are relatively prime.Corollary 2 to Shortcut 2: If the difference between the two numbers is 2 and the numbers are not even numbers, they are relatively prime and have no common factor other than 1. If the difference is 2 and they are both even, the greatest common factor is 2.Example: Find the greatest common factor of 13 and 15.The difference is 2 and the numbers are not even, so the greatest common factor is 1. Example: Find the greatest common factor of 14 and 16.The difference is 2 and the numbers are even, so the greatest common factor is 2.Corollary 3 to Shortcut 2: If the difference between the two numbers is a prime number, either that number is the greatest common factor or 1 is the greatest common factor. Example: Find the greatest common factor of 40 and 69.The difference is 29, which is a prime number. Since 29 does not divide evenly into both 40 and 69, the greatest common factor is 1, which means they are relatively prime. Example: Find the greatest common factor of 91 and 104.The difference is 13, which is a prime number. Since 13 divides evenly into both 91 and 104, the greatest common factor is 13.91 ÷ 13 = 7104 ÷ 13 = 8 Shortcut 3: If one of the numbers is prime, either it is the greatest common factor or the greatest common factor is 1. (Its only factors are 1 and itself, so those are the only possible common factors it could have with another number.)Example: Find the greatest common factor of 83 and 90.83 is a prime number and it is not a factor of 90, so the greatest common factor is 1. Example: Find the greatest common factor of 41 and 246.41 is a prime number and it is a factor of 246, so the greatest common factor is 41.246 ÷ 41 is 6---- Divisibility Rules:To determine the prime factors, it is sometimes helpful to use the divisibility rules.2: The number ends in 0, 2, 4, 6, or 8.Examples: 14, 58, 100, 33363: The sum of the number's digits is divisible by 3.Examples: 78 (7+8=15 which is divisible by 3), 114 (1+1+4=6 which is divisible by 3)5: The number ends in 0 or 5.Examples: 70, 195, 48607: The last digit doubled subtracted from the rest of the number is divisible by 7 or is equal to 0.Examples: 343 (3x2=6; 34-6=28 which is divisible by 7), 875 (5x2=10; 87-10=77 which is divisible by 7)11: Start with the left-most digit, subtract the next one, add the next one, subtract the next one, etc., and the final result is divisible by 11 or is equal to 0.Examples: 165 (1-6+5=0), 308 (3-0+8=11 which is divisible by 11), 1078 (1-0+7-8=0)Prime Numbers: Prime factors are prime numbers. The first 25 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
What are the steps in finding the least common multiple of two numbers?
to find the least common multiple of two numbers you must list the factors then you can find out their least common multiple of the two numbers
What is the greatest common factor of 372 and 510?
the greatest common factor between 372 and 510 is 6Two methods I can suggest:Find the prime factors of each number, collate and multiply together the common prime factors:372 = 2 x 2 x 3 x 31 510 = 2 x 3 x 5 x 17common prime factors = 2, 3Greatest Common Factor = 2 x 3 = 6To collate the common prime factors, it is often easier to mark each pair found (for example lightly crossing off or underlining)In collating the common factors, every time a pair appears the factor is noted; for example CGF of 36 and 48:36 = 2 x 2 x 3 x 348 = 2 x 2 x 2 x 2 x 3common prime factors = 2, 2, 3GCF = 2 x 2 x 3 = 12Euclid's method: Divide the larger by the smallerIgnoring the quotient, look at the remainderIf remainder is zero, the divisor (smaller of the two numbers) is the GCFOtherwise, repeat steps 1-3 with the divisor (smaller number) and the remainder510 / 372 = 1 r 138372 / 138 = 2 r 96138 / 96 = 1 r 4296 / 42 = 2 r 1242 / 12 = 3 r 612 / 6 = 2 r 0GCF = 6
What are the steps to find the hcf of 144 180 192?
The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 The factors of 180 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 The factors of 192 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192 The common factors are: 1, 2, 3, 4, 6, 12 The Greatest Common Factor: GCF = 12
What is the definition of algorithm?
The definition of the word algorithm is a set of rules for solving a problem in a finite number of steps, as for finding the greatest common divisor.
What are the steps of finding the Greatest common factor of 40 and 125?
Step 1. Factor them.2 x 2 x 2 x 5 = 405 x 5 x 5 = 125Step 2. Select the common factor.The GCF is 5.
What are the steps for rewriting expressions?
There are a few steps to rewriting expressions. The steps of rewriting expressions are finding the value of the letter and then using the common factor.
What is the greatest common factor steps for 7m14m?
If one term is a factor of the other, it is automatically the GCF. 7m is a factor of 14m and the GCF of this problem.
What are the steps for greatest common factor?
Step 1 : Prime Factorise each number and write in index notation. Step 2 : Multiply the lowest power of each common factor of the given numbers
Why is it easier to divide the numerator and denomenator by the gcf rather than any other number when simplifying a fraction?
It is preferable because this is the purpose, the ultimate aim, of simplification. You can only simplify to the extent that the greatest common factor will allow. You can do so in one step by finding the greatest common factor, or you can do so in multiple steps by first dividing by a lower factor (when you are finished you will see that all the lower factors multiply to give the gcf). Sometimes it is easier to do the task in multiple steps rather than searching for the gcf, but if you can identify the gcf then your simplification will be done in just one step.
What are the steps in finding the common monomial factor?
It is similar to finding the greatest common factor only you may have variables involved, so you may factor a constant and variable(s) which all terms are divisible by, for example: The common monomial factor in the following: 5x^2+5x would be 5x because both terms are divisible by 5 and x. 5x (x+1). Just find the constant and variable all terms are divisible by and then the product of those is your common monomial factor.
What is the steps to greatest common factor?
Example: 30 and 42Step 1: Factor them.2 x 3 x 5 = 302 x 3 x 7 = 42Step 2: Select the common factors.2 x 3 = 6, the GCF
What is the trick to finding the greatest common factor?
The following answer describes four methods of finding the greatest common factor, with examples, and several "tricks" or shortcuts that can make it easier.Method: Guess and RefineSometimes, you can look at two numbers and make a good guess that you can refine.Example 1: Find the greatest common factor of 45 and 50.Because both numbers end in either a 5 or 0, you know that they are both divisible by 5. If you divide both numbers by 5 and the results have no common factors (except 1), 5 is the greatest common factor.45 ÷ 5 = 950 ÷ 5 = 10Since 9 and 10 are consecutive numbers, they have no common factors. Therefore, the greatest common factor is 5.Example 2: Find the greatest common factor of 150 and 750.Both numbers end in 50, so they are both divisible by 50. If you divide both numbers by 50 and the results have another common factor, you continue identifying common factors until you have a pair without common factors.150 ÷ 50 = 3750 ÷ 50 = 15Since 15 is divisible by 3, and 3 is divisible by 3, you have another common factor, which is 3. Then, you can divide the most recent results by 3.3 ÷ 3 = 115 ÷ 3 = 5Since 1 and 5 do not have any common factors, take the two factors that you did identify, 50 and 3, and multiply them together: 50 x 3 = 150. This number, 150, is the greatest common factor.Method: Find All the FactorsIf the numbers are small enough or you know that they have only a few factors, you can list all the factors of each number and compare to determine the largest factor they have in common. One of the related questions links will take you to a page with the complete list of factors for numbers 1 through 100.Example: Find the greatest common factor of 15 and 18.The factors of 15 are 1, 3, 5, and 15.The factors of 18 are 1, 2, 3, 6, 9, and 18.The common factors are 1 and 3, so the greatest common factor is 3.Example: Find the greatest common factor of 26 and 91.The factors of 26 are 1, 2, 13, and 26.The factors of 91 are 1, 7, 13, and 91.The common factors are 1 and 13, so the greatest common factor is 13.Method: Find the Prime FactorsIn situations where you cannot get a good start simply by looking at the numbers, follow the following steps:1. Determine the prime factors of each number. See the related question "How do you find prime factors" for a method on doing this. Also, one of the related questions links will take you to a page with the complete list of prime factors for numbers 1 through 100.2. Determine the prime factors they have in common.3. Multiply all the prime factors they have in common to calculate the greatest common factor. Example: Find the greatest common factor of 5,544 and 37,620.The prime factors of 5,544 are 2, 2, 2, 3, 3, 7, and 11.The prime factors of 37,620 are 2, 2, 3, 3, 5, 11, and 19.The common prime factors are 2, 2, 3, 3, and 11.Therefore, the greatest common factor is 2 x 2 x 3 x 3 x 11 = 396. Example: Find the greatest common factor of 7,888 and 10,002.The prime factors of 7,888 are 2, 2, 2, 2, 17, and 29.The prime factors of 10,002 are 2, 3, and 1667.The common prime factors are a single 2.Therefore, the greatest common factor is 2. Method: Euclidean AlgorithmThis method is more efficient than finding the prime factors when the numbers are large, but teachers might prefer that you gain experience determining the prime factors of numbers. For this method, divide the larger number by the smaller number, then divide the "divisor" from the previous division by the remainder from the previous division, and continue until a number divides evenly. That divisor is the greatest common factor. Example: Find the greatest common factor of 33 and 77.77 ÷ 33 = 2 remainder 1133 ÷ 11 = 3 with no remainderSo, the final divisor, 11, is the greatest common factor. Example: Find the greatest common factor of 27 and 168.168 ÷ 27 = 6 remainder 627 ÷ 6 = 4 remainder 36 ÷ 3 = 2 with no remainderSo, the final divisor, 3, is the greatest common factor.---- Shortcut 1: If one number is a multiple of the other, the smaller number is the greatest common factor, because it is the largest possible factor of itself.Example: Find the greatest common factor of 72 and 288.288 is divisible by 72, therefore 72 is the greatest common factor.Shortcut 2: The greatest common factor of two numbers cannot be larger than the difference between the two numbers. So, you only need to test the numbers that are equal to or less than the difference between those two numbers. Also, the greatest common factor must be a factor of the difference between the two numbers. (This shortcut can help with finding the greatest common factor of three or more numbers. Examples are shown in the related question on finding the greatest common factor of three or more numbers.)Example: Find the greatest common factor of 56 and 64.The difference between 56 and 64 is 64 - 56 = 8. The largest possible common factor is the difference itself. So, check whether 8 divides evenly into both of them.56 ÷ 8 = 764 ÷ 8 = 8Therefore, 8 is the greatest common factor. Example: Find the greatest common factor of 72 and 88.The difference between 88 and 72 is 88 - 72 = 16. Check whether 16 divides evenly into both of them. It does not. But, the greatest common factor must be a factor of 16. The factors of 16 are 1, 2, 4, 8, and 16. So, try the next largest factor, 8, and see if it divides evenly into both of them.72 ÷ 8 = 988 ÷ 8 = 11Therefore, 8 is the greatest common factor.Example: Find the greatest common factor of 1003 and 1180.The difference between 1180 and 1003 is 177. Check whether 177 divides evenly into both of them. It does not. But, the greatest common factor must be a factor of 177. By using the divisibility rule for 3, you know that 3 is a factor of 177, but the divisibility rule indicates that neither 1003 nor 1180 are divisible by 3. 177 ÷ 3 = 59, so check 59 as a factor of both numbers. Note that 3 and 59 are both prime numbers, so they are the only prime factors of 177, so if there is a greatest common factor of 1003 and 1180 other than 1, since we have ruled out 177 and 3, it must be 59.1003 ÷ 59 = 171180 ÷ 59 = 20Therefore, 59 is the greatest common factor. Corollary 1 to Shortcut 2: If the numbers are only one number apart, they are relatively prime and have no common factor other than 1. Example: Find the greatest common factor of 4 and 5.The difference is 1, so the greatest common factor is 1. They are relatively prime.Corollary 2 to Shortcut 2: If the difference between the two numbers is 2 and the numbers are not even numbers, they are relatively prime and have no common factor other than 1. If the difference is 2 and they are both even, the greatest common factor is 2.Example: Find the greatest common factor of 13 and 15.The difference is 2 and the numbers are not even, so the greatest common factor is 1. Example: Find the greatest common factor of 14 and 16.The difference is 2 and the numbers are even, so the greatest common factor is 2.Corollary 3 to Shortcut 2: If the difference between the two numbers is a prime number, either that number is the greatest common factor or 1 is the greatest common factor. Example: Find the greatest common factor of 40 and 69.The difference is 29, which is a prime number. Since 29 does not divide evenly into both 40 and 69, the greatest common factor is 1, which means they are relatively prime. Example: Find the greatest common factor of 91 and 104.The difference is 13, which is a prime number. Since 13 divides evenly into both 91 and 104, the greatest common factor is 13.91 ÷ 13 = 7104 ÷ 13 = 8 Shortcut 3: If one of the numbers is prime, either it is the greatest common factor or the greatest common factor is 1. (Its only factors are 1 and itself, so those are the only possible common factors it could have with another number.)Example: Find the greatest common factor of 83 and 90.83 is a prime number and it is not a factor of 90, so the greatest common factor is 1. Example: Find the greatest common factor of 41 and 246.41 is a prime number and it is a factor of 246, so the greatest common factor is 41.246 ÷ 41 is 6---- Divisibility Rules:To determine the prime factors, it is sometimes helpful to use the divisibility rules.2: The number ends in 0, 2, 4, 6, or 8.Examples: 14, 58, 100, 33363: The sum of the number's digits is divisible by 3.Examples: 78 (7+8=15 which is divisible by 3), 114 (1+1+4=6 which is divisible by 3)5: The number ends in 0 or 5.Examples: 70, 195, 48607: The last digit doubled subtracted from the rest of the number is divisible by 7 or is equal to 0.Examples: 343 (3x2=6; 34-6=28 which is divisible by 7), 875 (5x2=10; 87-10=77 which is divisible by 7)11: Start with the left-most digit, subtract the next one, add the next one, subtract the next one, etc., and the final result is divisible by 11 or is equal to 0.Examples: 165 (1-6+5=0), 308 (3-0+8=11 which is divisible by 11), 1078 (1-0+7-8=0)Prime Numbers: Prime factors are prime numbers. The first 25 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
How can you factor a polynomial in standard form completely?
You can factor a polynomial using one of these steps: 1. Factor out the greatest common monomial factor. 2. Look for a difference of two squares or a perfect square trinomial. 3. Factor polynomials in the form ax^2+bx+c into a product of binomials. 4. Factor a polynomial with 4 terms by grouping.
What are the steps in solving the greatest odd factor?
Step 1: List all the factors. Step 2: Choose the largest odd number.
What are the methods in finding the GCF of numbers?
To find the greatest common factor (GCF) you can use one of a few methods. One way (which i think is the hardest) you list all the factors of those two numbers. Another way is to just multiply the numbers together. Now, if you have big numbers, these steps might be a little complicated or harder to do, but if you want to list all the factors of that number, go right ahead.
