GCF for 18, 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 18, 45 and 63?

Answer

GCF of 18, 45 and 63 is
9

(Nine)

9 is the largest positive integer that divides 18, 45 and 63 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 18, 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

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 factor184563Lowest power
22———
332323232
5—5——
7——7—

GCF = 3 × 3 = 9

Checking the GCF of 18, 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(18, 45) = 9

GCF(9, 63) = 9

GCF(18, 45, 63) = 9

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

18 ÷ 9 = 2

45 ÷ 9 = 5

63 ÷ 9 = 7

2, 5 and 7 have no common factor left — that is what makes 9 the greatest one.

Related Calculations

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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 18, 45 and 63? (The answer is: 9). Enter the first number (e.g. '18'), 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
1845483
1845491
1845501
1845513
1845521
1845531
1845549
1845551
1845561
1845573
1845581
1845591
1845603
1845611
1845621
1845639
1845641
1845651
1845663
1845671
1845681
1845693
1845701
1845711
1845729
1845731
1845741
1845753
1845761
1845771

FAQ

What's the Greatest Common Factor (GCF) of 18, 45 and 63?

GCF of 18, 45 and 63 is 9

What prime factors do 18, 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 18, 45 and 63 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 18 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 18 : 45 : 63?

Divide every term by the GCF 9: 18 ÷ 9 = 2, 45 ÷ 9 = 5 and 63 ÷ 9 = 7. So 18 : 45 : 63 in lowest terms is 2 : 5 : 7, and no whole number other than 1 divides all three of those.

See Also