GCF for 12, 24 and 36

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
and

What's the Greatest Common Factor (GCF) of 12, 24 and 36?

Answer

GCF of 12, 24 and 36 is
12

(Twelve)

12 is the largest positive integer that divides 12, 24 and 36 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 12, 24 and 36 by Prime Factorization

Split all three numbers into prime factors, then keep every prime that appears in all three of them, each taken as many times as it appears in the poorest factorization. Multiplying what is left gives the greatest common factor:

All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

Prime factor122436Lowest power
222232222
333323

GCF = 2 × 2 × 3 = 12

Checking the GCF of 12, 24 and 36 Two Numbers at a Time

The greatest common factor is associative, so three numbers can be handled as two pairs — and this is what makes the Euclidean algorithm usable here: run it on the first pair, then run it again on that result and the third number.

GCF(a, b, c) = GCF(GCF(a, b), c)

GCF(12, 24) = 12

GCF(12, 36) = 12

GCF(12, 24, 36) = 12

The answer checks out by division — all three quotients come out whole:

12 ÷ 12 = 1

24 ÷ 12 = 2

36 ÷ 12 = 3

1, 2 and 3 have no common factor left — that is what makes 12 the greatest one.

Related Calculations

See Also

About "Greatest Common Factor of 3 Numbers" Calculator

This calculator finds the Greatest Common Factor (GCF) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Greatest Common Factor (GCF) of 12, 24 and 36? (The answer is: 12). Enter the first number (e.g. '12'), the second (e.g. '24') and the third (e.g. '36'), then hit the 'Calculate' button.
The Greatest Common Factor of three numbers — also called the greatest common divisor (GCD) or highest common factor (HCF) — is the largest positive integer that divides all three of them with zero remainder
"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
and

GCF Table

Number 1Number 2Number 3GCF
1221243
1222242
1223241
12242412
1224251
1224262
1224273
1224284
1224291
1224306
1224311
1224324
1224333
1224342
1224351
12243612
1224371
1224382
1224393
1224404
1224411
1224426
1224431
1224444
1224453
1224462
1224471
12244812
1224491
1224502

FAQ

What's the Greatest Common Factor (GCF) of 12, 24 and 36?

GCF of 12, 24 and 36 is 12

What prime factors do 12, 24 and 36 share?

All three factorizations contain 2 × 2 × 3, and multiplying those shared primes gives 12 — exactly the greatest common factor.

Can you get the GCF of 12, 24 and 36 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 12 and 24 is 12, and the GCF of 12 and 36 is 12 — the same answer, because the greatest common factor is associative and does not depend on the order of the three numbers.

How does the GCF simplify the ratio 12 : 24 : 36?

Divide every term by the GCF 12: 12 ÷ 12 = 1, 24 ÷ 12 = 2 and 36 ÷ 12 = 3. So 12 : 24 : 36 in lowest terms is 1 : 2 : 3, and no whole number other than 1 divides all three of those.

See Also