GCF (HCF) of 120 and 210

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What is the Greatest Common Divisor of 120 and 210?

Answer

GCF (HCF) of 120 and 210 is
30

Common factors: 1, 2, 3, 5, 6, 10, 15, 30

30 divides both: 120 ÷ 30 = 4, 210 ÷ 30 = 7 — and 4 and 7 share no factor but 1, so no larger number divides both.

120 = 23 × 3 × 5

210 = 2 × 3 × 5 × 7

Prime120210Lowest power
22322
3333
5555
7—7—

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

GCF = 2 × 3 × 5 = 30

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GCF Table

Number 1Number 2GCF
12019515
1201964
1201971
1201986
1201991
12020040
1202013
1202022
1202031
12020412
1202055
1202062
1202073
1202088
1202091
12021030
1202111
1202124
1202133
1202142
1202155
12021624
1202171
1202182
1202193
12022020
1202211
1202226
1202231
1202248

FAQ

What is the Greatest Common Divisor of 120 and 210?

GCF (HCF) of 120 and 210 is 30

How to find the GCF of 120 and 210?

You can find the GCF of 120 and 210 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 120 and 210 is 30.

What prime factors do 120 and 210 share?

The prime factorizations of 120 and 210 have 2 × 3 × 5 in common, and multiplying those shared primes gives 30 — exactly the greatest common factor.

How does the GCF reduce the fraction 120/210?

Divide the numerator and the denominator by the GCF 30: 120 ÷ 30 = 4 and 210 ÷ 30 = 7. So 120/210 in lowest terms is 4/7.

See Also