SAT Math : How to find the greatest common factor

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #21 : Factors / Multiples

What's the greatest common factor of 81 and 27?

Possible Answers:

Correct answer:

Explanation:

Let's do some divisibility rules. For , the sum of the digits must be divisible by .

We have:

 They are both good so when we divide both numbers by , we get . Lastly they are both divisible by . So we multiply both factors to get an answer of .

Example Question #81 : Integers

What's the greatest common factor of 2, 6, 9, and 10?

Possible Answers:

Correct answer:

Explanation:

Greatest common factor involves all the numbers in the set. Even though three of the numbers are divisble by  isn't. The only factor that satisfies all the numbers is 

Example Question #23 : Factors / Multiples

What's the greatest common factor of 4, 8, 16, and 26?

Possible Answers:

Correct answer:

Explanation:

Although the first three numbers are divisible by  doesn't divide evenly into . The next best factor is . The remainder will be . This won't go any further as most of the numbers are even except . Our final answer is just .

Example Question #81 : Integers

What's the greatest common factor of 15, 90, 105, and 225?

Possible Answers:

Correct answer:

Explanation:

We know all of the numbers are divisible by  so when we divide all the numbers by , we have . Next, we can divide al of them by , because the sum of the digits of all numbers are divisible by . So we get . This is as best as we can go so now we multiply the factors to get  as an answer. 

Example Question #731 : Arithmetic

What's the greatest common factor of 36, 84, 96, 120, and 264?

Possible Answers:

Correct answer:

Explanation:

Because they are all even and divisible by , we can divide each number  to get . Next, let's divide by  to get . We are finished as we have a mixture of prime and composite numbers. We multiply the factors to get .

Example Question #11 : How To Find The Greatest Common Factor

Find the greatest common factor of and .

Possible Answers:

Correct answer:

Explanation:

The key here is to find the prime factorizations of both numbers and multiplying the common prime factors together:

Both prime factorizations have in common, so is our answer.

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