GCF for 15, 20 and 42

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
and

What's the Greatest Common Factor (GCF) of 15, 20 and 42?

Answer

GCF of 15, 20 and 42 is
1

(One)

1 is the largest positive integer that divides 15, 20 and 42 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 15, 20 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 15: 3 × 5 (exponent form: 3 × 5)

All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

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

Prime factor152042Lowest power
2—222—
33—3—
555——
7——7—

Not one prime factor is shared by all three numbers, which makes 15, 20 and 42 relatively prime as a set. The only positive integer dividing all of them is 1.

Checking the GCF of 15, 20 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(15, 20) = 5

GCF(5, 42) = 1

GCF(15, 20, 42) = 1

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

15 ÷ 1 = 15

20 ÷ 1 = 20

42 ÷ 1 = 42

15, 20 and 42 have no common factor left — that is what makes 1 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 15, 20 and 42? (The answer is: 1). Enter the first number (e.g. '15'), the second (e.g. '20') 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
1520271
1520281
1520291
1520305
1520311
1520321
1520331
1520341
1520355
1520361
1520371
1520381
1520391
1520405
1520411
1520421
1520431
1520441
1520455
1520461
1520471
1520481
1520491
1520505
1520511
1520521
1520531
1520541
1520555
1520561

FAQ

What's the Greatest Common Factor (GCF) of 15, 20 and 42?

GCF of 15, 20 and 42 is 1

What prime factors do 15, 20 and 42 share?

None at all: 15, 20 and 42 have no prime factor in common, so the only positive integer dividing all three is 1 and their GCF is 1.

Can you get the GCF of 15, 20 and 42 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 15 and 20 is 5, and the GCF of 5 and 42 is 1 — 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 15 : 20 : 42?

Divide every term by the GCF 1: 15 ÷ 1 = 15, 20 ÷ 1 = 20 and 42 ÷ 1 = 42. So 15 : 20 : 42 in lowest terms is 15 : 20 : 42, and no whole number other than 1 divides all three of those.

See Also