Practice Greatest Common Factor in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The greatest common factor (GCF) of two or more numbers is the largest positive integer that divides each of them evenly, with no remainder. It is also called the greatest common divisor (GCD).

The biggest 'piece' size that fits evenly into two numbers—like the largest tile that covers both a 12-unit and 18-unit floor.

Showing a random 20 of 50 problems.

Example 1

easy
Find the GCF of 12 and 18.

Example 2

medium
Find the GCF of 72⋅11 and 7⋅112.

Example 3

challenge
Find integers x,y such that gcd⁡(56,15)=56x+15y.

Example 4

easy
Find the GCF of 48 and 36.

Example 5

medium
Find the GCF of 48 and 36 using prime factorization.

Example 6

easy
Find the GCF of 60 and 45.

Example 7

medium
What is gcd⁡(0,17)?

Example 8

hard
Find gcd⁡(45,75,90).

Example 9

easy
Find the GCF of 32 and 48.

Example 10

medium
Find the GCF of 84, 126, and 210.

Example 11

hard
A rectangular floor of 24 ft by 36 ft is to be tiled with identical square tiles, no cutting. Find the largest tile side length.

Example 12

easy
A teacher has ribbons of lengths 24 cm and 36 cm. She wants to cut them into the longest equal pieces with no leftover. How long should each piece be?

Example 13

hard
Two consecutive integers always have what GCF?

Example 14

easy
Two numbers are coprime when their GCF is what?

Example 15

medium
Reduce 3648 using the GCF.

Example 16

easy
Find the GCF of 18 and 24.

Example 17

challenge
Use the Euclidean algorithm to find gcd⁡(48,18).

Example 18

easy
Find the GCF of 16 and 24.

Example 19

easy
Find the GCF of 30 and 50.

Example 20

easy
Find the GCF of 9 and 6.
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