GCF for 18, 24 and 36

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
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What's the Greatest Common Factor (GCF) of 18, 24 and 36?

Answer

GCF of 18, 24 and 36 is
6

(Six)

6 is the largest positive integer that divides 18, 24 and 36 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 18, 24 and 36 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 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

Prime factor182436Lowest power
2223222
3323323

GCF = 2 × 3 = 6

Checking the GCF of 18, 24 and 36 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, 24) = 6

GCF(6, 36) = 6

GCF(18, 24, 36) = 6

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

18 ÷ 6 = 3

24 ÷ 6 = 4

36 ÷ 6 = 6

3, 4 and 6 have no common factor left — that is what makes 6 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, 24 and 36? (The answer is: 6). Enter the first number (e.g. '18'), the second (e.g. '24') and the third (e.g. '36'), 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
1821243
1822242
1823241
1824246
1824251
1824262
1824273
1824282
1824291
1824306
1824311
1824322
1824333
1824342
1824351
1824366
1824371
1824382
1824393
1824402
1824411
1824426
1824431
1824442
1824453
1824462
1824471
1824486
1824491
1824502

FAQ

What's the Greatest Common Factor (GCF) of 18, 24 and 36?

GCF of 18, 24 and 36 is 6

What prime factors do 18, 24 and 36 share?

All three factorizations contain 2 × 3, and multiplying those shared primes gives 6 — exactly the greatest common factor.

Can you get the GCF of 18, 24 and 36 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 18 and 24 is 6, and the GCF of 6 and 36 is 6 — 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 : 24 : 36?

Divide every term by the GCF 6: 18 ÷ 6 = 3, 24 ÷ 6 = 4 and 36 ÷ 6 = 6. So 18 : 24 : 36 in lowest terms is 3 : 4 : 6, and no whole number other than 1 divides all three of those.

See Also