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.
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.
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.
120 and 140 have lots of common factors. e.g. 10, 5, 1, 20 You probably need to find the Highest common factor which is 20. But if you are doing your homework you probably need to show how you worked it out: 1 - Find the prime factors for each number 2 - Write the ones that appear in both in a list 3 - Multiply the numbers in your list
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.
To find all common multiples of two numbers, you first need to split them into their prime factors: 21 = 3x7 14 = 2x7 The next step is to identify any common factors. In this case, both numbers have 7 as a factor so we can discard one 7. Take every other prime factor (2, 3 and 7) and multiply them together to get the LCM: 2x3x7=42 To find any other common multiple, you simply multiply this number by an integer (2,3,4...). By doing this, you find that the first few numbers that 21 and 14 both go into are: 42, 84, 126, 168...
You should be doing this unaided as I am sure it is the Scottish Junior Maths Challenge!
You DO need a common denominator to add, subtract, or compare fractions. You DO NOT need a common denominator to multiply or divide fractions.
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.
Keep dividing top and bottom by any factor common to both. Here, 4 is an obvious factor. Some people would say 12 is even more obvious. Keep on doing it until you can no longer find any common factor.
When you're doing simple base premium, just multiply the base premium byt the rating factor. So 109.20 x 1.95, which is 212.94.
The common factor that seems to mark the conversion of a crowd into mob is known as mob mentality. This means that the people of the group will follow whatever the majority is doing, whether it is right or wrong.
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.
1 cm = 10 mm (multiply by 10) 1 mm = 0.1 cm (divide by 10) The conversion factor is 10, but be careful about what direction you're doing the conversion.
If you mean what is the Least Common Multiple (LCM) of 3, 7, 8, and 6 because they are denominators of fractions that you want to add, then here's how I go about doing it: First, 6 is a multiple of 3, so we don't have to worry about 3. Next, 8 = 2*2*2, and 6 = 3*2; they have one 2 & 1 in common, so you take the common factor and multiply by the other factors: 3*2*2*2 = 24. Then find the LCM of 24 and 7. The only common factor between them is 1, so the answer is 7 * 24 = 168.
To multiply by 0.75 you have to think about what your doing then you have to do the multiplication to get your answer.
To change a number into a percentage multiply it by 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.)
Doing my job
When doing fractions, you may cross multiply.
for area you times width x length
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
you multiply when you are finding the volume of something is because that is how you find how much space something takes