GCF for 15, 45 and 75

"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 75?

Answer

GCF of 15, 45 and 75 is
15

(Fifteen)

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

Finding the GCF of 15, 45 and 75 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 75: 3 × 5 × 5 (exponent form: 3 × 52)

Prime factor154575Lowest power
333233
555525

GCF = 3 × 5 = 15

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

GCF(15, 45, 75) = 15

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

15 ÷ 15 = 1

45 ÷ 15 = 3

75 ÷ 15 = 5

1, 3 and 5 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 15, 45 and 75? (The answer is: 15). Enter the first number (e.g. '15'), the second (e.g. '45') and the third (e.g. '75'), 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
15456015
1545611
1545621
1545633
1545641
1545655
1545663
1545671
1545681
1545693
1545705
1545711
1545723
1545731
1545741
15457515
1545761
1545771
1545783
1545791
1545805
1545813
1545821
1545831
1545843
1545855
1545861
1545873
1545881
1545891

FAQ

What's the Greatest Common Factor (GCF) of 15, 45 and 75?

GCF of 15, 45 and 75 is 15

What prime factors do 15, 45 and 75 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 15, 45 and 75 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 75 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 15 : 45 : 75?

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

See Also