GCF for 45, 75 and 90

"Greatest Common Factor of 3 Numbers" Calculator
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

(Fifteen)

15 is the largest positive integer that divides 45, 75 and 90 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 45, 75 and 90 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 45: 3 × 3 × 5 (exponent form: 32 × 5)

All Prime Factors of 75: 3 × 5 × 5 (exponent form: 3 × 52)

All Prime Factors of 90: 2 × 3 × 3 × 5 (exponent form: 2 × 32 × 5)

Prime factor457590Lowest power
2——2—
3323323
555255

GCF = 3 × 5 = 15

Checking the GCF of 45, 75 and 90 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(45, 75) = 15

GCF(15, 90) = 15

GCF(45, 75, 90) = 15

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

45 ÷ 15 = 3

75 ÷ 15 = 5

90 ÷ 15 = 6

3, 5 and 6 have no common factor left — that is what makes 15 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 45, 75 and 90? (The answer is: 15). Enter the first number (e.g. '45'), the second (e.g. '75') and the third (e.g. '90'), 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
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, and it is the check this page prints. 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