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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 Refine
Sometimes, 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 = 9
50 ÷ 5 = 10
Since 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 = 3
750 ÷ 50 = 15
Since 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 = 1
15 ÷ 3 = 5
Since 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 Factors
If 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 Factors
In 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 Algorithm
This 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 11
33 ÷ 11 = 3 with no remainder
So, the final divisor, 11, is the greatest common factor. Example: Find the greatest common factor of 27 and 168.
168 ÷ 27 = 6 remainder 6
27 ÷ 6 = 4 remainder 3
6 ÷ 3 = 2 with no remainder
So, 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 = 7
64 ÷ 8 = 8
Therefore, 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 = 9
88 ÷ 8 = 11
Therefore, 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 = 17
1180 ÷ 59 = 20
Therefore, 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 = 7
104 ÷ 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, 3336
3: 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, 4860
7: 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.
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Common factor of 45 20 56?
I would guess either that is a trick question or the answer is 1.
Factor x2 - x - 30?
x2 - x - 30 = (x - 6)(x + 5) The trick is to look for 2 numbers which multiply together to give -30 and sum together to give -1. In this case -6 and 5.
What is the trick to find the gcf of 1596 and 7182?
The factors of 1596 are: 1, 2, 3, 4, 6, 7, 12, 14, 19, 21, 28, 38, 42, 57, 76, 84, 114, 133, 228, 266, 399, 532, 798, 1596The factors of 7182 are: 1, 2, 3, 6, 7, 9, 14, 18, 19, 21, 27, 38, 42, 54, 57, 63, 114, 126, 133, 171, 189, 266, 342, 378, 399, 513, 798, 1026, 1197, 2394, 3591, 7182The common factors are: 1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 114, 133, 266, 399, 798The Greatest Common Factor (GCF) is: 798
How would you test to see whether 7 is a factor of 291?
There is no trick to find out easily if 7 is a factor of a given number, like 291. There are easy rules for finding out if 3 is a factor of a given number (adding up the digits, again and again until you have a single digit and then see if the single digit is a multiple of 3 or not: 291 includes digits 2, 9, 1 2 + 9 + 1 = 12 1 + 2 = 3 3 is a multiple of 3, so 291 is a multiple of 3. Indeed 291 = 3 x 97).For 7, the only was is to work out the division directly and see if there is any remainder or not: 291 / 7 = 41 remainder 4 thus 291 is not a multiple of 7, which is the same as saying that 7 is not a factor of 291.----------Actually there is a way to find whether a number has a factor of 7. It is discussed in Arthur Benjamin's "Secrets of Mental Math" Book, mental division, page 100. It states:Add or substract multiples of 7 to leave the last digit position as zero, then eliminate and continue until nothing is left.Example with 52925292 ends in 2, 6X7 42, substract 425292 -42 5250, eliminate the zero525, ends in 5 7x5 35, substract525-35490, eliminate the zero.49, which we know is a multiple of 7 (7^2). > 5292 is a multiple of 7.Another example16184, ends in 4, substract 1416170>1617 ends in 7, you can also add up to zero. Add 631680 >168, ends in 8, substract 28140> 14 which is divisible by 7. This number has a factor of 7.291 , last digit is one, 3x7 21, substract.291 - 21 250 > 25 which is not a multiple of 7. > 291 does not have a factor of 7.
What is the smallest number which when subtracted from an even number gives an odd number?
2-1=1 so i guess 1, is this a trick question?
What is the trick to finding the greatest common factors?
Finding the GCF will help you when you are trying to reduce fractions.
What is the trick to finding the least common multiple?
Prime factor tree!
How do you find the common factors and the greatest common factor of two numbers?
you divide the number by itself then you add the same number onto it and then divide by 3. this is a very uselful trick that my maths teacher, mr plunkstick, told me
Common factor of 45 20 56?
I would guess either that is a trick question or the answer is 1.
What is the trick to finding the least common denominator?
Example: 30 and 42 Factor them. 2 x 3 x 5 = 30 2 x 3 x 7 = 42 Select the highest amount of each factor. 2 x 3 x 5 x 7 = 210, the LCM
What is the trick to finding the greatest common factor of three or more numbers?
The standard ways of determining the greatest common factor of three or more numbers is* to compare all their factors and choose the largest one that is common to all, or * to compare their prime factors and multiply together all the ones that are common to all, or * to determine the greatest common factor two numbers at a time.However, you can also look at the difference between the numbers being compared. The greatest common factor cannot be greater than the smallest difference between the numbers. Also, the greatest common factor must be a factor of the difference between the numbers.Example: Find the greatest common factor of 8, 10, and 14.The difference between 8 and 10 is 2, which means the greatest common factor cannot be greater than 2. (The difference between 10 and 14 is 4 and the difference between 8 and 14 is 6, both of which are divisible by 2, so 2 remains a possible greatest common factor.) So, check whether 2 evenly divides 8, 10, and 14. It does, so 2 is the greatest common factor.Example: Find the greatest common factor of 84, 91, and 105.The difference between 84 and 91 is 7, which means the greatest common factor cannot be greater than 7. (The difference between 91 and 105 is 14 and the difference between 105 and 84 is 21, both of which are divisible by 7, so 7 remains a possible greatest common factor.) So, check whether 7 evenly divides 84, 91, and 105. It does, so 7 is the greatest common factor. Here are the factors for those numbers so you can see that it is correct:The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.The factors of 91 are 1, 7, 13, and 91.The factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105.More Complex Example: Find the greatest common factor of 42, 54, and 66.The difference between 42 and 54 is 12, which is also the same difference between 54 and 66, so the greatest common factor cannot be greater than 12. So, check whether 12 evenly divides 42, 54, and 66. It does not, so try the largest factor of 12 that is less than 12, which is 6. Check whether 6 divides evenly 42, 54, and 66. It does, so 6 is the greatest common factor. Here are the factors for those numbers so you can see that it is correct:The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66.More Complex Example: Find the greatest common factor of 36, 42, and 76.The difference between 36 and 42 is 8. The difference between 42 and 76 is 34. Since the greatest common factor must be a factor of the difference, we can examine these smaller numbers, 8 and 34, to see if they have a factor in common. The only factor they have in common (excluding 1) is 2. Since 2 evenly divides 36, 42, and 76, it is the greatest common factor. Here are the factors for those numbers so you can see that it is correct:The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.The factors of 76 are 1, 2, 4, 19, 38, and 76.Four Numbers Example: Find the greatest common factor of 27, 39, 54, and 60.The difference between 27 and 39 is 12. The difference between 39 and 54 is 15. The difference between 54 and 60 is 6. Since the greatest common factor must be a factor of the difference, we can examine these smaller numbers, 12, 15, and 6, to see if they have a factor in common. The only factor they have in common (excluding 1) is 3. Since 3 evenly divides 27, 39, 54, and 60, it is the greatest common factor. Here are the factors for those numbers so you can see that it is correct:The factors of 27 are 1, 3, 9, and 27.The factors of 39 are 1, 3, 13, and 39.The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.The same way as with two. You can list the factors and find the common ones or compare their prime factorizations.
Is 24 a factor of 96?
It is a factor (96/6=16). There is a trick that can help you remember if 6 is a factor. It has to be divisible by two (ie if it ends in a even number) and be divisible by 3. The trick for finding if it's divisible by three is to add up all of its digits. In this case, you would do 9+6, which gives you 15. If you do that again (1+5), that gives you 6, which is a known multiple of three.
What is a good trick for simplifying fractions?
Break each part of the fraction down into prime numbers and then remove the prime numbers that make up the greatest common factor. What you are left with is the reduced fraction. 10/30 10 = 1 x 2 x 5 30 = 1 x 2 x 3 x 5 GCF = 2 x 5 = 10 The greatest common factor numbers are 2 & 5; when these numbers are removed you are left with 1/3, which is 10/30 reduced.
What is criss angel's greatest trick?
Levitating and walking on water are 2 of his greatest tricks.
What is the trick to finding the lowest common multiple?
Example: 30 and 42 Factor them. 2 x 3 x 5 = 30 2 x 3 x 7 = 42 Combine the factors, eliminating duplicates. 2 x 3 x 5 x 7 = 210, the LCM
Is there a trick to finding the fifth item in collections on Cafe World?
No..
What is the greatest magic trick in the world?
life and death game
