GCF for 35, 56 and 63

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
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What's the Greatest Common Factor (GCF) of 35, 56 and 63?

Answer

GCF of 35, 56 and 63 is
7

(Seven)

7 is the largest positive integer that divides 35, 56 and 63 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 35, 56 and 63 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 35: 5 × 7 (exponent form: 5 × 7)

All Prime Factors of 56: 2 × 2 × 2 × 7 (exponent form: 23 × 7)

All Prime Factors of 63: 3 × 3 × 7 (exponent form: 32 × 7)

Prime factor355663Lowest power
2—23——
3——32—
55———
77777

GCF = 7 = 7

Checking the GCF of 35, 56 and 63 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(35, 56) = 7

GCF(7, 63) = 7

GCF(35, 56, 63) = 7

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

35 ÷ 7 = 5

56 ÷ 7 = 8

63 ÷ 7 = 9

5, 8 and 9 have no common factor left — that is what makes 7 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 35, 56 and 63? (The answer is: 7). Enter the first number (e.g. '35'), the second (e.g. '56') and the third (e.g. '63'), 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
3548561
3549567
3550561
3551561
3552561
3553561
3554561
3555561
3556567
3556571
3556581
3556591
3556601
3556611
3556621
3556637
3556641
3556651
3556661
3556671
3556681
3556691
3556707
3556711
3556721
3556731
3556741
3556751
3556761
3556777

FAQ

What's the Greatest Common Factor (GCF) of 35, 56 and 63?

GCF of 35, 56 and 63 is 7

What prime factors do 35, 56 and 63 share?

All three factorizations contain 7, and multiplying those shared primes gives 7 — exactly the greatest common factor.

Can you get the GCF of 35, 56 and 63 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 35 and 56 is 7, and the GCF of 7 and 63 is 7 — 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 35 : 56 : 63?

Divide every term by the GCF 7: 35 ÷ 7 = 5, 56 ÷ 7 = 8 and 63 ÷ 7 = 9. So 35 : 56 : 63 in lowest terms is 5 : 8 : 9, and no whole number other than 1 divides all three of those.

See Also