GCF for 10, 12 and 15

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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

Common factors: 1

Only 1 divides all three: no prime is a factor of each of 10, 12 and 15.

Pairs do share factors — GCF(10, 12) = 2, GCF(10, 15) = 5, GCF(12, 15) = 3 — just none greater than 1 common to all three.

10 = 2 × 5

12 = 22 × 3

15 = 3 × 5

Prime101215Lowest power
2222——
3—33—
55—5—

— = power 0: the prime is not a factor of this number, so it cannot be in the GCF.

GCF = 1

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GCF Table

1st2nd3rdGCF
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. 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.

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