GCF for 12, 30 and 42

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
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What's the Greatest Common Factor (GCF) of 12, 30 and 42?

Answer

GCF of 12, 30 and 42 is
6

(Six)

6 is the largest positive integer that divides 12, 30 and 42 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 12, 30 and 42 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

All Prime Factors of 42: 2 × 3 × 7 (exponent form: 2 × 3 × 7)

Prime factor123042Lowest power
222222
33333
5—5——
7——7—

GCF = 2 × 3 = 6

Checking the GCF of 12, 30 and 42 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(12, 30) = 6

GCF(6, 42) = 6

GCF(12, 30, 42) = 6

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

12 ÷ 6 = 2

30 ÷ 6 = 5

42 ÷ 6 = 7

2, 5 and 7 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 12, 30 and 42? (The answer is: 6). Enter the first number (e.g. '12'), the second (e.g. '30') and the third (e.g. '42'), 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
1227303
1228302
1229301
1230306
1230311
1230322
1230333
1230342
1230351
1230366
1230371
1230382
1230393
1230402
1230411
1230426
1230431
1230442
1230453
1230462
1230471
1230486
1230491
1230502
1230513
1230522
1230531
1230546
1230551
1230562

FAQ

What's the Greatest Common Factor (GCF) of 12, 30 and 42?

GCF of 12, 30 and 42 is 6

What prime factors do 12, 30 and 42 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 12, 30 and 42 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 12 and 30 is 6, and the GCF of 6 and 42 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 12 : 30 : 42?

Divide every term by the GCF 6: 12 ÷ 6 = 2, 30 ÷ 6 = 5 and 42 ÷ 6 = 7. So 12 : 30 : 42 in lowest terms is 2 : 5 : 7, and no whole number other than 1 divides all three of those.

See Also