GCF for 6, 12 and 15

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

What's the Greatest Common Factor (GCF) of 6, 12 and 15?

Answer

GCF of 6, 12 and 15 is
3

(Three)

3 is the largest positive integer that divides 6, 12 and 15 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 6, 12 and 15 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 6: 2 × 3 (exponent form: 2 × 3)

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

All Prime Factors of 15: 3 × 5 (exponent form: 3 × 5)

Prime factor61215Lowest power
2222——
33333
5——5—

GCF = 3 = 3

Checking the GCF of 6, 12 and 15 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(6, 12) = 6

GCF(6, 15) = 3

GCF(6, 12, 15) = 3

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

6 ÷ 3 = 2

12 ÷ 3 = 4

15 ÷ 3 = 5

2, 4 and 5 have no common factor left — that is what makes 3 the greatest one.

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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 6, 12 and 15? (The answer is: 3). Enter the first number (e.g. '6'), the second (e.g. '12') and the third (e.g. '15'), 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
16121
26122
36123
46122
56121
66126
67121
68122
69123
610122
611121
612126
612131
612142
612153
612162
612171
612186
612191
612202
612213
612222
612231
612246
612251
612262
612273
612282
612291
612306

FAQ

What's the Greatest Common Factor (GCF) of 6, 12 and 15?

GCF of 6, 12 and 15 is 3

What prime factors do 6, 12 and 15 share?

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

Can you get the GCF of 6, 12 and 15 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 6 and 12 is 6, and the GCF of 6 and 15 is 3 — 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 6 : 12 : 15?

Divide every term by the GCF 3: 6 ÷ 3 = 2, 12 ÷ 3 = 4 and 15 ÷ 3 = 5. So 6 : 12 : 15 in lowest terms is 2 : 4 : 5, and no whole number other than 1 divides all three of those.

See Also