GCF for 45, 60 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 45, 60 and 75?

Answer

GCF of 45, 60 and 75 is
15

(Fifteen)

15 is the largest positive integer that divides 45, 60 and 75 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 45, 60 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 45: 3 × 3 × 5 (exponent form: 32 × 5)

All Prime Factors of 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

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

Prime factor456075Lowest power
2—22——
332333
555525

GCF = 3 × 5 = 15

Checking the GCF of 45, 60 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(45, 60) = 15

GCF(15, 75) = 15

GCF(45, 60, 75) = 15

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

45 ÷ 15 = 3

60 ÷ 15 = 4

75 ÷ 15 = 5

3, 4 and 5 have no common factor left — that is what makes 15 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 45, 60 and 75? (The answer is: 15). Enter the first number (e.g. '45'), the second (e.g. '60') 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
45606015
4560611
4560621
4560633
4560641
4560655
4560663
4560671
4560681
4560693
4560705
4560711
4560723
4560731
4560741
45607515
4560761
4560771
4560783
4560791
4560805
4560813
4560821
4560831
4560843
4560855
4560861
4560873
4560881
4560891

FAQ

What's the Greatest Common Factor (GCF) of 45, 60 and 75?

GCF of 45, 60 and 75 is 15

What prime factors do 45, 60 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 45, 60 and 75 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 45 and 60 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 45 : 60 : 75?

Divide every term by the GCF 15: 45 ÷ 15 = 3, 60 ÷ 15 = 4 and 75 ÷ 15 = 5. So 45 : 60 : 75 in lowest terms is 3 : 4 : 5, and no whole number other than 1 divides all three of those.

See Also