GCF (HCF) of 60 and 420

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What is the Greatest Common Divisor of 60 and 420?

Answer

GCF (HCF) of 60 and 420 is
60

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

60 divides 420 (420 ÷ 60 = 7), so the GCF is the smaller number itself.

60 = 22 × 3 × 5

420 = 22 × 3 × 5 × 7

Prime60420Lowest power
2222222
3333
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
6017010
601755
6018060
601855
6019515
6020020
602055
6021030
6022020
6022515
602455
6025010
6026020
602755
6029010
603255
603355
603555
6037515
603855
6039030
6040020
6042060
604255
6043010
6043515
6045030
6046020
6047010
6049515

FAQ

What is the Greatest Common Divisor of 60 and 420?

GCF (HCF) of 60 and 420 is 60

How to find the GCF of 60 and 420?

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

What prime factors do 60 and 420 share?

The prime factorizations of 60 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 60/420?

Divide the numerator and the denominator by the GCF 60: 60 ÷ 60 = 1 and 420 ÷ 60 = 7. So 60/420 in lowest terms is 1/7.

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