GCF Calculator · Practical guide
GCF of 24 and 36
The greatest common factor of 24 and 36 is 12 — here is exactly why, two different ways.
At a glance
The Answer: 12
The greatest common factor of 24 and 36 is 12. It is the largest number that divides both 24 and 36 evenly: 24 ÷ 12 = 2 and 36 ÷ 12 = 3. Enter any pair of numbers in the calculator above to get the same breakdown instantly.
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Results
Method 1: Prime Factorization
Break each number into primes:
- 24 = 2 × 2 × 2 × 3
- 36 = 2 × 2 × 3 × 3
The shared prime factors are two 2s and one 3. Multiply them together: 2 × 2 × 3 = 12. The calculator shows this prime factorization for every number you enter.
Method 2: Euclidean Algorithm
Repeatedly divide and take remainders:
- gcd(36, 24): 36 mod 24 = 12
- gcd(24, 12): 24 mod 12 = 0
- Result = 12
When the remainder hits zero, the last divisor is the GCF. This method is fast even for very large numbers where listing factors would be tedious.
Listing All Common Factors
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The factors they share are 1, 2, 3, 4, 6, and 12 — and the greatest of these is 12.
Frequently Asked Questions
What is the LCM of 24 and 36?
The least common multiple of 24 and 36 is 72. A handy identity: LCM equals the product of the two numbers divided by the GCF, so 24 times 36 divided by 12 equals 72.
Are GCF and GCD the same thing?
Yes. Greatest Common Factor and Greatest Common Divisor are two names for the same value — the largest integer that divides all the given numbers evenly.
Can I find the GCF of more than two numbers?
Yes. Enter three or more numbers separated by commas and the calculator finds the GCF of the entire set, applying the Euclidean algorithm pairwise.
What if the numbers share no factors besides 1?
Then the GCF is 1 and the numbers are called coprime or relatively prime. For example, the GCF of 8 and 15 is 1.