GCF for 120, 144 and 324

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
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What's the Greatest Common Factor (GCF) of 120, 144 and 324?

Answer

GCF of 120, 144 and 324 is
12

(Twelve)

12 is the largest positive integer that divides 120, 144 and 324 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 120, 144 and 324 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 120: 2 × 2 × 2 × 3 × 5 (exponent form: 23 × 3 × 5)

All Prime Factors of 144: 2 × 2 × 2 × 2 × 3 × 3 (exponent form: 24 × 32)

All Prime Factors of 324: 2 × 2 × 3 × 3 × 3 × 3 (exponent form: 22 × 34)

Prime factor120144324Lowest power
223242222
3332343
55———

GCF = 2 × 2 × 3 = 12

Checking the GCF of 120, 144 and 324 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(120, 144) = 24

GCF(24, 324) = 12

GCF(120, 144, 324) = 12

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

120 ÷ 12 = 10

144 ÷ 12 = 12

324 ÷ 12 = 27

10, 12 and 27 have no common factor left — that is what makes 12 the greatest one.

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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 120, 144 and 324? (The answer is: 12). Enter the first number (e.g. '120'), the second (e.g. '144') and the third (e.g. '324'), 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
1201443093
1201443102
1201443111
12014431224
1201443131
1201443142
1201443153
1201443164
1201443171
1201443186
1201443191
1201443208
1201443213
1201443222
1201443231
12014432412
1201443251
1201443262
1201443273
1201443288
1201443291
1201443306
1201443311
1201443324
1201443333
1201443342
1201443351
12014433624
1201443371
1201443382

FAQ

What's the Greatest Common Factor (GCF) of 120, 144 and 324?

GCF of 120, 144 and 324 is 12

What prime factors do 120, 144 and 324 share?

All three factorizations contain 2 × 2 × 3, and multiplying those shared primes gives 12 — exactly the greatest common factor.

Can you get the GCF of 120, 144 and 324 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 120 and 144 is 24, and the GCF of 24 and 324 is 12 — 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 120 : 144 : 324?

Divide every term by the GCF 12: 120 ÷ 12 = 10, 144 ÷ 12 = 12 and 324 ÷ 12 = 27. So 120 : 144 : 324 in lowest terms is 10 : 12 : 27, and no whole number other than 1 divides all three of those.

See Also