GCF for 18, 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 18, 30 and 42?

Answer

GCF of 18, 30 and 42 is
6

(Six)

6 is the largest positive integer that divides 18, 30 and 42 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 18, 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

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 factor183042Lowest power
22222
332333
5—5——
7——7—

GCF = 2 × 3 = 6

Checking the GCF of 18, 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(18, 30) = 6

GCF(6, 42) = 6

GCF(18, 30, 42) = 6

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

18 ÷ 6 = 3

30 ÷ 6 = 5

42 ÷ 6 = 7

3, 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 18, 30 and 42? (The answer is: 6). Enter the first number (e.g. '18'), 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
1827303
1828302
1829301
1830306
1830311
1830322
1830333
1830342
1830351
1830366
1830371
1830382
1830393
1830402
1830411
1830426
1830431
1830442
1830453
1830462
1830471
1830486
1830491
1830502
1830513
1830522
1830531
1830546
1830551
1830562

FAQ

What's the Greatest Common Factor (GCF) of 18, 30 and 42?

GCF of 18, 30 and 42 is 6

What prime factors do 18, 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 18, 30 and 42 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 18 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 18 : 30 : 42?

Divide every term by the GCF 6: 18 ÷ 6 = 3, 30 ÷ 6 = 5 and 42 ÷ 6 = 7. So 18 : 30 : 42 in lowest terms is 3 : 5 : 7, and no whole number other than 1 divides all three of those.

See Also