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

(Five)

5 is the largest positive integer that divides 10, 30 and 45 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 10, 30 and 45 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

Prime factor103045Lowest power
222——
3—332—
55555

GCF = 5 = 5

Checking the GCF of 10, 30 and 45 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, 30) = 10

GCF(10, 45) = 5

GCF(10, 30, 45) = 5

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

10 ÷ 5 = 2

30 ÷ 5 = 6

45 ÷ 5 = 9

2, 6 and 9 have no common factor left — that is what makes 5 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, 30 and 45? (The answer is: 5). Enter the first number (e.g. '10'), the second (e.g. '30') and the third (e.g. '45'), 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
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, and it is the check this page prints. 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