Lesson 5: Greatest Common Factor — Practice Questions

1. 1. Which of the following pairs of numbers has a greatest common factor (GCF) of 8?

   • A. (16, 32)
   • B. (24, 40)
   • C. (16, 20)
   • D. (12, 20)

2. 2. The GCF of 18 and another number is 6. If the other number is greater than 18, what is its smallest possible value? The other number is ___.

3. 3. A pair of numbers is created with a GCF of 15 by multiplying 15 by the coprime numbers 2 and 7. One number is 30. The other number is ___.

4. 4. To create a pair of numbers with a GCF of 10, we multiply 10 by two numbers, $x$ and $y$. Which condition must be true for $x$ and $y$?

   • A. x and y must both be prime
   • B. x and y must be coprime
   • C. x and y must both be even
   • D. x must be a factor of y

5. 5. A student tries to find a pair of numbers with a GCF of 5. They multiply 5 by 4 and 6. The resulting numbers are 20 and 30. The actual GCF of this pair is ___.

6. 6. What is the greatest common factor (GCF) of 45 and 60? The GCF is ___.

7. 7. The prime factorization of 56 is $2^3 \cdot 7$ and 98 is $2 \cdot 7^2$. What is the GCF of 56 and 98?

   • A. $2 \cdot 7$
   • B. $2^3 \cdot 7^2$
   • C. $2 \cdot 7^2$
   • D. $2^3 \cdot 7$

8. 8. Using prime factorization, find the greatest common factor (GCF) of 70 and 98. The GCF is ___.

9. 9. Which statement best defines the greatest common factor (GCF) of two numbers?

   • A. The smallest number that is a multiple of both numbers.
   • B. The largest number that divides evenly into both numbers.
   • C. The product of all the prime factors from both numbers.
   • D. The smallest prime factor shared by both numbers.

10. 10. The sum $36 + 54$ can be simplified using the GCF. This can be rewritten as a product in the form $\_\_\_(2+3)$.