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GCF (HCF) of 72 and 120

"Greatest Common Factor" Calculator

What is the Greatest Common Divisor of 72 and 120?

Answer

GCF (HCF) of 72 and 120 is

24

Common factors: 1, 2, 3, 4, 6, 8, 12, 24

24 divides both: 72 ÷ 24 = 3, 120 ÷ 24 = 5 — and 3 and 5 share no factor but 1, so no larger number divides both.

72 = 2³ × 3²

120 = 2³ × 3 × 5

Prime	72	120	Lowest power
2	2³	2³	2³
3	3²	3	3
5	—	5	—

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

GCF = 2³ × 3 = 24

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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 72 and 120. The GCF of 72 and 120 is 24 — 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
72	105	3
72	106	2
72	107	1
72	108	36
72	109	1
72	110	2
72	111	3
72	112	8
72	113	1
72	114	6
72	115	1
72	116	4
72	117	9
72	118	2
72	119	1
72	120	24
72	121	1
72	122	2
72	123	3
72	124	4
72	125	1
72	126	18
72	127	1
72	128	8
72	129	3
72	130	2
72	131	1
72	132	12
72	133	1
72	134	2

FAQ

What is the Greatest Common Divisor of 72 and 120?

GCF (HCF) of 72 and 120 is 24

How to find the GCF of 72 and 120?

You can find the GCF of 72 and 120 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 72 and 120 is 24.

What prime factors do 72 and 120 share?

The prime factorizations of 72 and 120 have 2 × 2 × 2 × 3 in common, and multiplying those shared primes gives 24 — exactly the greatest common factor.

How does the GCF reduce the fraction 72/120?

Divide the numerator and the denominator by the GCF 24: 72 ÷ 24 = 3 and 120 ÷ 24 = 5. So 72/120 in lowest terms is 3/5.