GCF (HCF) of 120 and 180

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What is the Greatest Common Divisor of 120 and 180?

Answer

GCF (HCF) of 120 and 180 is
60

Common factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

60 divides both: 120 ÷ 60 = 2, 180 ÷ 60 = 3 — and 2 and 3 share no factor but 1, so no larger number divides both.

120 = 23 × 3 × 5

180 = 22 × 32 × 5

Prime120180Lowest power
2232222
33323
5555

GCF = 22 × 3 × 5 = 60

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GCF Table

Number 1Number 2GCF
12016515
1201662
1201671
12016824
1201691
12017010
1201713
1201724
1201731
1201746
1201755
1201768
1201773
1201782
1201791
12018060
1201811
1201822
1201833
1201848
1201855
1201866
1201871
1201884
1201893
12019010
1201911
12019224
1201931
1201942

FAQ

What is the Greatest Common Divisor of 120 and 180?

GCF (HCF) of 120 and 180 is 60

How to find the GCF of 120 and 180?

You can find the GCF of 120 and 180 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 120 and 180 is 60.

What prime factors do 120 and 180 share?

The prime factorizations of 120 and 180 have 2 × 2 × 3 × 5 in common, and multiplying those shared primes gives 60 — exactly the greatest common factor.

How does the GCF reduce the fraction 120/180?

Divide the numerator and the denominator by the GCF 60: 120 ÷ 60 = 2 and 180 ÷ 60 = 3. So 120/180 in lowest terms is 2/3.

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