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 1212 and 1818.

Example 2

medium
Find the GCF of 72⋅117^2\cdot11 and 7⋅1127\cdot11^2.

Example 3

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

Example 4

easy
Find the GCF of 4848 and 3636.

Example 5

medium
Find the GCF of 4848 and 3636 using prime factorization.

Example 6

easy
Find the GCF of 6060 and 4545.

Example 7

medium
What is gcd⁡(0,17)\gcd(0, 17)?

Example 8

hard
Find gcd⁡(45,75,90)\gcd(45, 75, 90).

Example 9

easy
Find the GCF of 3232 and 4848.

Example 10

medium
Find the GCF of 8484, 126126, and 210210.

Example 11

hard
A rectangular floor of 2424 ft by 3636 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 2424 cm and 3636 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\frac{36}{48} using the GCF.

Example 16

easy
Find the GCF of 1818 and 2424.

Example 17

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

Example 18

easy
Find the GCF of 1616 and 2424.

Example 19

easy
Find the GCF of 3030 and 5050.

Example 20

easy
Find the GCF of 99 and 66.
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