GCF for 18, 39 and 45

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
and

What's the Greatest Common Factor (GCF) of 18, 39 and 45?

Answer

GCF of 18, 39 and 45 is
3

(Three)

3 is the largest positive integer that divides 18, 39 and 45 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 18, 39 and 45 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 39: 3 × 13 (exponent form: 3 × 13)

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

Prime factor183945Lowest power
22———
3323323
5——5—
13—13——

GCF = 3 = 3

Checking the GCF of 18, 39 and 45 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, 39) = 3

GCF(3, 45) = 3

GCF(18, 39, 45) = 3

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

18 ÷ 3 = 6

39 ÷ 3 = 13

45 ÷ 3 = 15

6, 13 and 15 have no common factor left — that is what makes 3 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 18, 39 and 45? (The answer is: 3). Enter the first number (e.g. '18'), the second (e.g. '39') and the third (e.g. '45'), 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
1830393
1831391
1832391
1833393
1834391
1835391
1836393
1837391
1838391
1839393
1839401
1839411
1839423
1839431
1839441
1839453
1839461
1839471
1839483
1839491
1839501
1839513
1839521
1839531
1839543
1839551
1839561
1839573
1839581
1839591

FAQ

What's the Greatest Common Factor (GCF) of 18, 39 and 45?

GCF of 18, 39 and 45 is 3

What prime factors do 18, 39 and 45 share?

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

Can you get the GCF of 18, 39 and 45 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 18 and 39 is 3, and the GCF of 3 and 45 is 3 — 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 : 39 : 45?

Divide every term by the GCF 3: 18 ÷ 3 = 6, 39 ÷ 3 = 13 and 45 ÷ 3 = 15. So 18 : 39 : 45 in lowest terms is 6 : 13 : 15, and no whole number other than 1 divides all three of those.

See Also