GCF for 10, 30 and 45

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
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What's the Greatest Common Factor (GCF) of 10, 30 and 45?

Answer

GCF of 10, 30 and 45 is
5

Common factors: 1, 5

5 divides all three: 10 ÷ 5 = 2, 30 ÷ 5 = 6, 45 ÷ 5 = 9 — and 2, 6 and 9 have no factor but 1 common to all of them, so no larger number divides all three.

10 = 2 × 5

30 = 2 × 3 × 5

45 = 32 × 5

Prime103045Lowest power
222——
3—332—
55555

— = 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
10303010
1030311
1030322
1030331
1030342
1030355
1030362
1030371
1030382
1030391
10304010
1030411
1030422
1030431
1030442
1030455
1030462
1030471
1030482
1030491
10305010
1030511
1030522
1030531
1030542
1030555
1030562
1030571
1030582
1030591

FAQ

What's the Greatest Common Factor (GCF) of 10, 30 and 45?

GCF of 10, 30 and 45 is 5

What prime factors do 10, 30 and 45 share?

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

Can you get the GCF of 10, 30 and 45 two numbers at a time?

Yes. The GCF of 10 and 30 is 10, and the GCF of 10 and 45 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 10 : 30 : 45?

Divide every term by the GCF 5: 10 ÷ 5 = 2, 30 ÷ 5 = 6 and 45 ÷ 5 = 9. So 10 : 30 : 45 in lowest terms is 2 : 6 : 9, and no whole number other than 1 divides all three of those.

See Also