GCF for 27, 45 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 27, 45 and 63?

Answer

GCF of 27, 45 and 63 is
9

(Nine)

9 is the largest positive integer that divides 27, 45 and 63 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 27, 45 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 27: 3 × 3 × 3 (exponent form: 33)

All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

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

Prime factor274563Lowest power
333323232
5—5——
7——7—

GCF = 3 × 3 = 9

Checking the GCF of 27, 45 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(27, 45) = 9

GCF(9, 63) = 9

GCF(27, 45, 63) = 9

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

27 ÷ 9 = 3

45 ÷ 9 = 5

63 ÷ 9 = 7

3, 5 and 7 have no common factor left — that is what makes 9 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 27, 45 and 63? (The answer is: 9). Enter the first number (e.g. '27'), the second (e.g. '45') 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
2745483
2745491
2745501
2745513
2745521
2745531
2745549
2745551
2745561
2745573
2745581
2745591
2745603
2745611
2745621
2745639
2745641
2745651
2745663
2745671
2745681
2745693
2745701
2745711
2745729
2745731
2745741
2745753
2745761
2745771

FAQ

What's the Greatest Common Factor (GCF) of 27, 45 and 63?

GCF of 27, 45 and 63 is 9

What prime factors do 27, 45 and 63 share?

All three factorizations contain 3 × 3, and multiplying those shared primes gives 9 — exactly the greatest common factor.

Can you get the GCF of 27, 45 and 63 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 27 and 45 is 9, and the GCF of 9 and 63 is 9 — 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 27 : 45 : 63?

Divide every term by the GCF 9: 27 ÷ 9 = 3, 45 ÷ 9 = 5 and 63 ÷ 9 = 7. So 27 : 45 : 63 in lowest terms is 3 : 5 : 7, and no whole number other than 1 divides all three of those.

See Also