GCF for 8, 12 and 42

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

Answer

GCF of 8, 12 and 42 is
2

Common factors: 1, 2

2 divides all three: 8 ÷ 2 = 4, 12 ÷ 2 = 6, 42 ÷ 2 = 21 — and 4, 6 and 21 have no factor but 1 common to all of them, so no larger number divides all three.

8 = 23

12 = 22 × 3

42 = 2 × 3 × 7

Prime81242Lowest power
2232222
3—33—
7——7—

— = power 0: the prime is not a factor of this number, so it cannot be in the GCF.

GCF = 2

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GCF Table

1st2nd3rdGCF
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. 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