GCF (HCF) of 180 and 420

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What is the Greatest Common Divisor of 180 and 420?

Answer

GCF (HCF) of 180 and 420 is
60

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

60 divides both: 180 ÷ 60 = 3, 420 ÷ 60 = 7 — and 3 and 7 share no factor but 1, so no larger number divides both.

180 = 22 × 32 × 5

420 = 22 × 3 × 5 × 7

Prime180420Lowest power
2222222
33233
5555
7—7—

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

GCF = 22 × 3 × 5 = 60

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GCF Table

Number 1Number 2GCF
18040545
1804062
1804071
18040812
1804091
18041010
1804113
1804124
1804131
18041418
1804155
1804164
1804173
1804182
1804191
18042060
1804211
1804222
1804239
1804244
1804255
1804266
1804271
1804284
1804293
18043010
1804311
18043236
1804331
1804342

FAQ

What is the Greatest Common Divisor of 180 and 420?

GCF (HCF) of 180 and 420 is 60

How to find the GCF of 180 and 420?

You can find the GCF of 180 and 420 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 180 and 420 is 60.

What prime factors do 180 and 420 share?

The prime factorizations of 180 and 420 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 180/420?

Divide the numerator and the denominator by the GCF 60: 180 ÷ 60 = 3 and 420 ÷ 60 = 7. So 180/420 in lowest terms is 3/7.

See Also