GCF for 15, 45 and 100

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
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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

(Five)

5 is the largest positive integer that divides 15, 45 and 100 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 15, 45 and 100 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 15: 3 × 5 (exponent form: 3 × 5)

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

All Prime Factors of 100: 2 × 2 × 5 × 5 (exponent form: 22 × 52)

Prime factor1545100Lowest power
2——22—
3332——
555525

GCF = 5 = 5

Checking the GCF of 15, 45 and 100 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(15, 45) = 15

GCF(15, 100) = 5

GCF(15, 45, 100) = 5

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

15 ÷ 5 = 3

45 ÷ 5 = 9

100 ÷ 5 = 20

3, 9 and 20 have no common factor left — that is what makes 5 the greatest one.

Related Calculations

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 15, 45 and 100? (The answer is: 5). Enter the first number (e.g. '15'), the second (e.g. '45') and the third (e.g. '100'), 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
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, and it is the check this page prints. 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.

See Also