GCF (HCF) of 100 and 120

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What is the Greatest Common Divisor of 100 and 120?

Answer

GCF (HCF) of 100 and 120 is
20

Common factors: 1, 2, 4, 5, 10, 20

20 divides both: 100 ÷ 20 = 5, 120 ÷ 20 = 6 — and 5 and 6 share no factor but 1, so no larger number divides both.

100 = 22 × 52

120 = 23 × 3 × 5

Prime100120Lowest power
2222322
3—3—
55255

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

GCF = 22 × 5 = 20

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GCF Table

Number 1Number 2GCF
100100100
1001055
10011010
10012020
1001211
10012525
1001355
10014020
1001444
1001455
10015050
10016020
1001655
10017010
10018020
1001855
10019010
100200100
1002055
10022020
10023010
1002355
10024020
1002455
10025050
10026020
10027010
10027525
10028020
10029010

FAQ

What is the Greatest Common Divisor of 100 and 120?

GCF (HCF) of 100 and 120 is 20

How to find the GCF of 100 and 120?

You can find the GCF of 100 and 120 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 100 and 120 is 20.

What prime factors do 100 and 120 share?

The prime factorizations of 100 and 120 have 2 × 2 × 5 in common, and multiplying those shared primes gives 20 — exactly the greatest common factor.

How does the GCF reduce the fraction 100/120?

Divide the numerator and the denominator by the GCF 20: 100 ÷ 20 = 5 and 120 ÷ 20 = 6. So 100/120 in lowest terms is 5/6.

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