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What is the greatest common factor of 45 and 56 by doing prime factorization?
Wiki User
∙ 9y ago
3 x 3 x 5 = 45
2 x 2 x 2 x 7 = 56
Since none of the prime factors are the same, the GCF is 1.
Wiki User
∙ 9y ago
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Do you put the bigger number in front or the smaller number in front when your doing prime factorization?
Smaller. It should run least to greatest.
What is the prime factorization of the composite number 42?
42=2x21 21=3x7 PF=2x3x7 The PF (Prime Factorization) of 42 is 2x3x7.(Sorry, I couldn't do a factor tree, there are always helpful to use when doing prime factorization, but since this is the computer, I could only do it like the following above.)
How do you solve distributive property problems?
You can solve distributive property problems, by doing this: Let's say your problem is 27+12. You start by doing this: What factor goes into 27? Wait... what Greatest Common Factor belongs to 27? It's 9. So, what you do is this: 3(9+?) 3*? equals 12? 3*4= 12. So it's 4. So, 3(9+4) 9+4= 13 3*13= 39 27 +12 equals 39
What does method mean in math?
A Way of doing something a Math. Example: The Prime Factorization Method.
What is the answer for 75 when doing factor tree?
75 25,3 5,5,3
Do you do factors of the greatest common factor or multiples?
When doing fractions it is the greatest common factor (GCF) and the least common multiple (LCM). You want the GCF when you are reducing fractions to their simplest form. When changing the denominators to a common one, you want the LCM.
Do you add or multiply when doing greatest common factor?
One place where this is used is to simplify fractions: you need to find the greatest common factor, then divide top and bottom by this greatest common factor.Also, in factoring expressions - you can take out the greatest common factor. For example (using "^" for power): 5x^2 + 10x has the greatest common factor 5x; so this can be taken out as a common factor, resulting in 5x(x + 2).
Does a factor have to be prime if you are doing prime factorization on a factor tree?
no because the prime factorization of 16 is 4 and 4 then 2 and 2 and 2 and 2 so they don't have to be prime
How do you find the GCF by doing a factor tree?
Factor trees are ways of finding the prime factorization of given numbers. Example: 30 and 42 30 15,2 5,3,2 42 21,2 7,3,2 Select the common factors. 2 x 3 = 6, the GCF.
Do you put the bigger number in front or the smaller number in front when your doing prime factorization?
Smaller. It should run least to greatest.
What is the greatest common factor of 22 and 66?
The greatest common factor of 22 and 66 can be done in a split second. I am assuming the person who asked this question knew that 2 x 3 = 6. Multiplication works in your favor. When doing 22 x 3, You do 2x 3, and then 2x 3 again, thus getting 66. The answer is therefore 22.
What is the greatest common factor of 42 and 98?
The greatest common factor is the highest number that divides exactly into two or more numbers.42: 1, 2, 3, 6, 7, 14, 21, 4298: 1, 2, 7, 14, 49, 98The GCF of 42 and 98 is 14.If you're not a good guesser the best way to go about doing this is to list all the factors of each number, like so:42-- 98--1 12 23 76 147142142Well, I did not list all the factors of 98, but I know that since 98 is not divisible by 21 or 42 that the greatest common factor is 14.Answer: 14
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 is the G.C.F of 28 and 100?
By Euclid's algorithm, that's the same as the gcf of 28 and 16 - where 16 is calculated as the remainder of 100 divided by 28. (You can continue by doing the division of 28 by 16; the next pair will be 16 and that remainder.)
How do you find the common factor in numbers?
You determine all numbers that will can be divided evenly (without a remainder) into the object numbers. The highest number doing that is the common factor.
What is the prime factorization of the composite number 42?
42=2x21 21=3x7 PF=2x3x7 The PF (Prime Factorization) of 42 is 2x3x7.(Sorry, I couldn't do a factor tree, there are always helpful to use when doing prime factorization, but since this is the computer, I could only do it like the following above.)
How do you reduce the fraction 36 over 54 to its lowest terms?
To reduce any fraction to its lowest terms, divide the numeratorand the denominator by their greatest common factor.You have 36/54.The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.The common factors are 1, 2, 3, 6, 9, and 18.The greatest common factor is 18 .36 / 18 = 254 / 18 = 336/54 = 2/3Note:That's why you had to spend all that time doing common factors andgreatest common factor before you could go on to doing fractions.
