GCF (HCF) of 42 and 105

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What is the Greatest Common Divisor of 42 and 105?

Answer

GCF (HCF) of 42 and 105 is

Common factors: 1, 3, 7, 21

21 divides both: 42 ÷ 21 = 2, 105 ÷ 21 = 5 — and 2 and 5 share no factor but 1, so no larger number divides both.

42 = 2 × 3 × 7

105 = 3 × 5 × 7

Prime	42	105	Lowest power
2	2	—	—
3	3	3	3
5	—	5	—
7	7	7	7

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

GCF = 3 × 7 = 21

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GCF Table

Number 1	Number 2	GCF
42	28	14
42	44	2
42	45	3
42	46	2
42	48	6
42	49	7
42	50	2
42	51	3
42	52	2
42	54	6
42	55	1
42	56	14
42	57	3
42	58	2
42	59	1
42	60	6
42	63	21
42	65	1
42	70	14
42	72	6
42	80	2
42	84	42
42	86	2
42	90	6
42	96	6
42	98	14
42	100	2
42	105	21
42	231	21
42	1,365	21

FAQ

What is the Greatest Common Divisor of 42 and 105?

GCF (HCF) of 42 and 105 is 21

How to find the GCF of 42 and 105?

You can find the GCF of 42 and 105 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 42 and 105 is 21.

What prime factors do 42 and 105 share?

The prime factorizations of 42 and 105 have 3 × 7 in common, and multiplying those shared primes gives 21 — exactly the greatest common factor.

How does the GCF reduce the fraction 42/105?

Divide the numerator and the denominator by the GCF 21: 42 ÷ 21 = 2 and 105 ÷ 21 = 5. So 42/105 in lowest terms is 2/5.

GCF (HCF) of 42 and 105

What is the Greatest Common Divisor of 42 and 105?

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See Also

GCF Table

FAQ

What is the Greatest Common Divisor of 42 and 105?

How to find the GCF of 42 and 105?

What prime factors do 42 and 105 share?

How does the GCF reduce the fraction 42/105?

See Also