GCF for 8, 12 and 42

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

What's the Greatest Common Factor (GCF) of 8, 12 and 42?

Answer

GCF of 8, 12 and 42 is
2

(Two)

2 is the largest positive integer that divides 8, 12 and 42 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 8, 12 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 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

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

Prime factor81242Lowest power
2232222
3—33—
7——7—

GCF = 2 = 2

Checking the GCF of 8, 12 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(8, 12) = 4

GCF(4, 42) = 2

GCF(8, 12, 42) = 2

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

8 ÷ 2 = 4

12 ÷ 2 = 6

42 ÷ 2 = 21

4, 6 and 21 have no common factor left — that is what makes 2 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 8, 12 and 42? (The answer is: 2). Enter the first number (e.g. '8'), the second (e.g. '12') 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
812271
812284
812291
812302
812311
812324
812331
812342
812351
812364
812371
812382
812391
812404
812411
812422
812431
812444
812451
812462
812471
812484
812491
812502
812511
812524
812531
812542
812551
812564

FAQ

What's the Greatest Common Factor (GCF) of 8, 12 and 42?

GCF of 8, 12 and 42 is 2

What prime factors do 8, 12 and 42 share?

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

Can you get the GCF of 8, 12 and 42 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 8 and 12 is 4, and the GCF of 4 and 42 is 2 — 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 8 : 12 : 42?

Divide every term by the GCF 2: 8 ÷ 2 = 4, 12 ÷ 2 = 6 and 42 ÷ 2 = 21. So 8 : 12 : 42 in lowest terms is 4 : 6 : 21, and no whole number other than 1 divides all three of those.

See Also