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GCF (HCF) of 32 and 72

"Greatest Common Factor" Calculator

What is the Greatest Common Divisor of 32 and 72?

Answer

GCF (HCF) of 32 and 72 is

8

Common factors: 1, 2, 4, 8

8 divides both: 32 ÷ 8 = 4, 72 ÷ 8 = 9 — and 4 and 9 share no factor but 1, so no larger number divides both.

32 = 2⁵

72 = 2³ × 3²

Prime	32	72	Lowest power
2	2⁵	2³	2³
3	—	3²	—

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

GCF = 2³ = 8

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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 32 and 72. The GCF of 32 and 72 is 8 — 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
32	33	1
32	34	2
32	35	1
32	36	4
32	38	2
32	40	8
32	41	1
32	42	2
32	44	4
32	45	1
32	46	2
32	48	16
32	49	1
32	50	2
32	52	4
32	54	2
32	55	1
32	56	8
32	57	1
32	58	2
32	60	4
32	72	8
32	80	16
32	81	1
32	84	4
32	90	2
32	96	32
32	128	32
32	176	16

FAQ

What is the Greatest Common Divisor of 32 and 72?

GCF (HCF) of 32 and 72 is 8

How to find the GCF of 32 and 72?

You can find the GCF of 32 and 72 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 32 and 72 is 8.

What prime factors do 32 and 72 share?

The prime factorizations of 32 and 72 have 2 × 2 × 2 in common, and multiplying those shared primes gives 8 — exactly the greatest common factor.

How does the GCF reduce the fraction 32/72?

Divide the numerator and the denominator by the GCF 8: 32 ÷ 8 = 4 and 72 ÷ 8 = 9. So 32/72 in lowest terms is 4/9.