GCF for 45, 75 and 90

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Greatest Common Factor of
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What's the Greatest Common Factor (GCF) of 45, 75 and 90?

Answer

GCF of 45, 75 and 90 is
15

Common factors: 1, 3, 5, 15

15 divides all three: 45 ÷ 15 = 3, 75 ÷ 15 = 5, 90 ÷ 15 = 6 — and 3, 5 and 6 have no factor but 1 common to all of them, so no larger number divides all three.

45 = 32 × 5

75 = 3 × 52

90 = 2 × 32 × 5

Prime457590Lowest power
2——2—
3323323
555255

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

GCF = 3 × 5 = 15

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GCF Table

1st2nd3rdGCF
45757515
4575761
4575771
4575783
4575791
4575805
4575813
4575821
4575831
4575843
4575855
4575861
4575873
4575881
4575891
45759015
4575911
4575921
4575933
4575941
4575955
4575963
4575971
4575981
4575993
45751005
45751011
45751023
45751031
45751041

FAQ

What's the Greatest Common Factor (GCF) of 45, 75 and 90?

GCF of 45, 75 and 90 is 15

What prime factors do 45, 75 and 90 share?

All three factorizations contain 3 × 5, and multiplying those shared primes gives 15 — exactly the greatest common factor.

Can you get the GCF of 45, 75 and 90 two numbers at a time?

Yes. The GCF of 45 and 75 is 15, and the GCF of 15 and 90 is 15 — 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 45 : 75 : 90?

Divide every term by the GCF 15: 45 ÷ 15 = 3, 75 ÷ 15 = 5 and 90 ÷ 15 = 6. So 45 : 75 : 90 in lowest terms is 3 : 5 : 6, and no whole number other than 1 divides all three of those.

See Also