GCF for 111, 324 and 432

"Greatest Common Factor of 3 Numbers" Calculator

What's the Greatest Common Factor (GCF) of 111, 324 and 432?

Answer

GCF of 111, 324 and 432 is

(Three)

3 is the largest positive integer that divides 111, 324 and 432 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 111, 324 and 432 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 111: 3 × 37 (exponent form: 3 × 37)

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

All Prime Factors of 432: 2 × 2 × 2 × 2 × 3 × 3 × 3 (exponent form: 2⁴ × 3³)

Prime factor	111	324	432	Lowest power
2	—	2²	2⁴	—
3	3	3⁴	3³	3
37	37	—	—	—

GCF = 3 = 3

Checking the GCF of 111, 324 and 432 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(111, 324) = 3

GCF(3, 432) = 3

GCF(111, 324, 432) = 3

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

111 ÷ 3 = 37

324 ÷ 3 = 108

432 ÷ 3 = 144

37, 108 and 144 have no common factor left — that is what makes 3 the greatest one.

Related Calculations

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 111, 324 and 432? (The answer is: 3). Enter the first number (e.g. '111'), the second (e.g. '324') and the third (e.g. '432'), 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

GCF Table

Number 1	Number 2	Number 3	GCF
111	324	417	3
111	324	418	1
111	324	419	1
111	324	420	3
111	324	421	1
111	324	422	1
111	324	423	3
111	324	424	1
111	324	425	1
111	324	426	3
111	324	427	1
111	324	428	1
111	324	429	3
111	324	430	1
111	324	431	1
111	324	432	3
111	324	433	1
111	324	434	1
111	324	435	3
111	324	436	1
111	324	437	1
111	324	438	3
111	324	439	1
111	324	440	1
111	324	441	3
111	324	442	1
111	324	443	1
111	324	444	3
111	324	445	1
111	324	446	1

FAQ

What's the Greatest Common Factor (GCF) of 111, 324 and 432?

GCF of 111, 324 and 432 is 3

What prime factors do 111, 324 and 432 share?

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

Can you get the GCF of 111, 324 and 432 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 111 and 324 is 3, and the GCF of 3 and 432 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 111 : 324 : 432?

Divide every term by the GCF 3: 111 ÷ 3 = 37, 324 ÷ 3 = 108 and 432 ÷ 3 = 144. So 111 : 324 : 432 in lowest terms is 37 : 108 : 144, and no whole number other than 1 divides all three of those.

GCF for 111, 324 and 432

What's the Greatest Common Factor (GCF) of 111, 324 and 432?

Finding the GCF of 111, 324 and 432 by Prime Factorization

Checking the GCF of 111, 324 and 432 Two Numbers at a Time

Related Calculations

See Also

About "Greatest Common Factor of 3 Numbers" Calculator

GCF Table

FAQ

What's the Greatest Common Factor (GCF) of 111, 324 and 432?

What prime factors do 111, 324 and 432 share?

Can you get the GCF of 111, 324 and 432 two numbers at a time?

How does the GCF simplify the ratio 111 : 324 : 432?

See Also

Number 1	Number 2	Number 3	GCF
111	324	417	3
111	324	418	1
111	324	419	1
111	324	420	3
111	324	421	1
111	324	422	1
111	324	423	3
111	324	424	1
111	324	425	1
111	324	426	3
111	324	427	1
111	324	428	1
111	324	429	3
111	324	430	1
111	324	431	1
111	324	432	3
111	324	433	1
111	324	434	1
111	324	435	3
111	324	436	1
111	324	437	1
111	324	438	3
111	324	439	1
111	324	440	1
111	324	441	3
111	324	442	1
111	324	443	1
111	324	444	3
111	324	445	1
111	324	446	1

Number 1	Number 2	Number 3	GCF
111	324	417	3
111	324	418	1
111	324	419	1
111	324	420	3
111	324	421	1
111	324	422	1
111	324	423	3
111	324	424	1
111	324	425	1
111	324	426	3
111	324	427	1
111	324	428	1
111	324	429	3
111	324	430	1
111	324	431	1
111	324	432	3
111	324	433	1
111	324	434	1
111	324	435	3
111	324	436	1
111	324	437	1
111	324	438	3
111	324	439	1
111	324	440	1
111	324	441	3
111	324	442	1
111	324	443	1
111	324	444	3
111	324	445	1
111	324	446	1

Number 1	Number 2	Number 3	GCF
111	324	417	3
111	324	418	1
111	324	419	1
111	324	420	3
111	324	421	1
111	324	422	1
111	324	423	3
111	324	424	1
111	324	425	1
111	324	426	3
111	324	427	1
111	324	428	1
111	324	429	3
111	324	430	1
111	324	431	1
111	324	432	3
111	324	433	1
111	324	434	1
111	324	435	3
111	324	436	1
111	324	437	1
111	324	438	3
111	324	439	1
111	324	440	1
111	324	441	3
111	324	442	1
111	324	443	1
111	324	444	3
111	324	445	1
111	324	446	1