GCF for 45, 70 and 85

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
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What's the Greatest Common Factor (GCF) of 45, 70 and 85?

Answer

GCF of 45, 70 and 85 is
5

(Five)

5 is the largest positive integer that divides 45, 70 and 85 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 45, 70 and 85 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 70: 2 × 5 × 7 (exponent form: 2 × 5 × 7)

All Prime Factors of 85: 5 × 17 (exponent form: 5 × 17)

Prime factor457085Lowest power
2—2——
332———
55555
7—7——
17——17—

GCF = 5 = 5

Checking the GCF of 45, 70 and 85 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, 70) = 5

GCF(5, 85) = 5

GCF(45, 70, 85) = 5

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

45 ÷ 5 = 9

70 ÷ 5 = 14

85 ÷ 5 = 17

9, 14 and 17 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 45, 70 and 85? (The answer is: 5). Enter the first number (e.g. '45'), the second (e.g. '70') and the third (e.g. '85'), 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
4570705
4570711
4570721
4570731
4570741
4570755
4570761
4570771
4570781
4570791
4570805
4570811
4570821
4570831
4570841
4570855
4570861
4570871
4570881
4570891
4570905
4570911
4570921
4570931
4570941
4570955
4570961
4570971
4570981
4570991

FAQ

What's the Greatest Common Factor (GCF) of 45, 70 and 85?

GCF of 45, 70 and 85 is 5

What prime factors do 45, 70 and 85 share?

All three factorizations contain 5, and multiplying those shared primes gives 5 — exactly the greatest common factor.

Can you get the GCF of 45, 70 and 85 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 45 and 70 is 5, and the GCF of 5 and 85 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 45 : 70 : 85?

Divide every term by the GCF 5: 45 ÷ 5 = 9, 70 ÷ 5 = 14 and 85 ÷ 5 = 17. So 45 : 70 : 85 in lowest terms is 9 : 14 : 17, and no whole number other than 1 divides all three of those.

See Also