GCF for 10, 12 and 15

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
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What's the Greatest Common Factor (GCF) of 10, 12 and 15?

Answer

GCF of 10, 12 and 15 is
1

(One)

1 is the largest positive integer that divides 10, 12 and 15 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 10, 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 10: 2 × 5 (exponent form: 2 × 5)

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

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

Prime factor101215Lowest power
2222——
3—33—
55—5—

Not one prime factor is shared by all three numbers, which makes 10, 12 and 15 relatively prime as a set. The only positive integer dividing all of them is 1.

Checking the GCF of 10, 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(10, 12) = 2

GCF(2, 15) = 1

GCF(10, 12, 15) = 1

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

10 ÷ 1 = 10

12 ÷ 1 = 12

15 ÷ 1 = 15

10, 12 and 15 have no common factor left — that is what makes 1 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 10, 12 and 15? (The answer is: 1). Enter the first number (e.g. '10'), 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
110121
210122
310121
410122
510121
610122
710121
810122
910121
1010122
1011121
1012122
1012131
1012142
1012151
1012162
1012171
1012182
1012191
1012202
1012211
1012222
1012231
1012242
1012251
1012262
1012271
1012282
1012291
1012302

FAQ

What's the Greatest Common Factor (GCF) of 10, 12 and 15?

GCF of 10, 12 and 15 is 1

What prime factors do 10, 12 and 15 share?

None at all: 10, 12 and 15 have no prime factor in common, so the only positive integer dividing all three is 1 and their GCF is 1.

Can you get the GCF of 10, 12 and 15 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 10 and 12 is 2, and the GCF of 2 and 15 is 1 — 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 10 : 12 : 15?

Divide every term by the GCF 1: 10 ÷ 1 = 10, 12 ÷ 1 = 12 and 15 ÷ 1 = 15. So 10 : 12 : 15 in lowest terms is 10 : 12 : 15, and no whole number other than 1 divides all three of those.

See Also