GCF for 15, 45 and 100

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What's the Greatest Common Factor (GCF) of 15, 45 and 100?

Answer

GCF of 15, 45 and 100 is
5

Common factors: 1, 5

5 divides all three: 15 ÷ 5 = 3, 45 ÷ 5 = 9, 100 ÷ 5 = 20 — and 3, 9 and 20 have no factor but 1 common to all of them, so no larger number divides all three.

15 = 3 × 5

45 = 32 × 5

100 = 22 × 52

Prime1545100Lowest power
2——22—
3332——
555525

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

GCF = 5

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GCF Table

1st2nd3rdGCF
1545855
1545861
1545873
1545881
1545891
15459015
1545911
1545921
1545933
1545941
1545955
1545963
1545971
1545981
1545993
15451005
15451011
15451023
15451031
15451041
154510515
15451061
15451071
15451083
15451091
15451105
15451113
15451121
15451131
15451143

FAQ

What's the Greatest Common Factor (GCF) of 15, 45 and 100?

GCF of 15, 45 and 100 is 5

What prime factors do 15, 45 and 100 share?

All three factorizations contain 5, and multiplying those shared primes gives 5 — exactly the greatest common factor.

Can you get the GCF of 15, 45 and 100 two numbers at a time?

Yes. The GCF of 15 and 45 is 15, and the GCF of 15 and 100 is 5 — 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 15 : 45 : 100?

Divide every term by the GCF 5: 15 ÷ 5 = 3, 45 ÷ 5 = 9 and 100 ÷ 5 = 20. So 15 : 45 : 100 in lowest terms is 3 : 9 : 20, and no whole number other than 1 divides all three of those.

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