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GCF (HCF) of 42 and 105

"Greatest Common Factor" Calculator

What is the Greatest Common Divisor of 42 and 105?

Answer

GCF (HCF) of 42 and 105 is

21

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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See Also

Least Common Multiple - Find the Least Common Multiple (LCM) of two numbers
Greatest Common Factor of 3 Numbers - Find the Greatest Common Factor (GCF) of three numbers
Least Common Multiple of 3 Numbers - Find the Least Common Multiple (LCM) of three numbers

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What is the GCF (HCF) of 42 and 105. The GCF of 42 and 105 is 21 — the biggest number that can divide both integers. Step-by-step GCF (GCD) calculation by factoring.

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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.