GCF (HCF) of 210 and 300

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What is the Greatest Common Divisor of 210 and 300?

Answer

GCF (HCF) of 210 and 300 is
30

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

30 divides both: 210 ÷ 30 = 7, 300 ÷ 30 = 10 — and 7 and 10 share no factor but 1, so no larger number divides both.

210 = 2 × 3 × 5 × 7

300 = 22 × 3 × 52

Prime210300Lowest power
22222
3333
55525
77——

— = 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
21028515
2102862
2102877
2102886
2102891
21029010
2102913
2102922
2102931
21029442
2102955
2102962
2102973
2102982
2102991
21030030
2103017
2103022
2103033
2103042
2103055
2103066
2103071
21030814
2103093
21031010
2103111
2103126
2103131
2103142

FAQ

What is the Greatest Common Divisor of 210 and 300?

GCF (HCF) of 210 and 300 is 30

How to find the GCF of 210 and 300?

You can find the GCF of 210 and 300 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 210 and 300 is 30.

What prime factors do 210 and 300 share?

The prime factorizations of 210 and 300 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 210/300?

Divide the numerator and the denominator by the GCF 30: 210 ÷ 30 = 7 and 300 ÷ 30 = 10. So 210/300 in lowest terms is 7/10.

See Also