Factor the First Number
Enter the complete prime factorization of the first number.
Free Interactive Math Tool
Greatest Common Factor Practice
Compare the prime factorizations of two numbers, identify every shared prime factor, multiply the common factors together, and find the greatest common factor step by step.
Learn How to Find the GCF First
Learn how factors, prime factorization, shared prime factors, and repeated factors are used to find the greatest common factor of two whole numbers.
Read the Greatest Common Factor GuideHow It Works
Find the GCF Step by Step
Break both numbers into prime factors, identify the prime factors they share, and multiply those shared factors to find the greatest common factor.
Factor the Second Number
Enter the complete prime factorization of the second number.
Match Shared Primes
Select only the prime factors that appear in both factorizations, including repeated copies.
Multiply the Common Factors
Multiply the shared prime factors to calculate the greatest common factor.
Interactive Practice
Greatest Common Factor
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Problems
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Find the greatest common factor of
48
60
Prime factorize both numbers, identify the shared prime factors, and multiply them to find the GCF.
1
First Number
2
Second Number
3
Shared Factors
4
Find GCF
Step 1
Prime factorize the first number.
Enter every prime factor of 48. Repeated prime factors must be entered more than once.
First Number
48
Separate factors with multiplication signs, commas, spaces, or the letter x.
Step 2
Prime factorize the second number.
Enter every prime factor of 60. Repeated prime factors must be entered more than once.
Second Number
60
Separate factors with multiplication signs, commas, spaces, or the letter x.
Step 3
Select the shared prime factors.
Compare the two prime factorizations. Select every prime factor that appears in both lists. Repeated copies must be matched one at a time.
Prime factors of 48
Prime factors of 60
Shared Prime Factors
Step 4
Multiply the shared factors.
Multiply the common prime factors you selected. Their product is the greatest common factor.
Common-factor product
Great job!
You found the greatest common factor correctly.
Helpful Reminders
Tips for Finding the Greatest Common Factor
Prime Factorize Completely
Keep factoring until every factor is prime before comparing the two numbers.
Match Repeated Factors
If a prime appears multiple times in both numbers, include only the copies they have in common.
Ignore Extra Factors
Prime factors that appear in only one number are not part of the greatest common factor.
Multiply the Shared Factors
The product of the shared prime factors is always the greatest common factor.
Why Learn This?
Where You'll Use the GCF
Simplifying Fractions
Divide the numerator and denominator by their greatest common factor to reduce fractions.
Algebra
Factoring algebraic expressions often begins by factoring out the greatest common factor.
Word Problems
The GCF is used whenever equal groups must be made without any leftovers.
Keep Practicing
Every new problem uses different numbers and provides immediate feedback so you can master greatest common factors with confidence.