GCF (HCF) of 200 and 300

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What is the Greatest Common Divisor of 200 and 300?

Answer

GCF (HCF) of 200 and 300 is
100

Common factors: 1, 2, 4, 5, 10, 20, 25, 50, 100

100 divides both: 200 ÷ 100 = 2, 300 ÷ 100 = 3 — and 2 and 3 share no factor but 1, so no larger number divides both.

200 = 23 × 52

300 = 22 × 3 × 52

Prime200300Lowest power
2232222
3—3—
5525252

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

GCF = 22 × 52 = 100

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GCF Table

Number 1Number 2GCF
2002855
2002862
2002871
2002888
2002891
20029010
2002911
2002924
2002931
2002942
2002955
2002968
2002971
2002982
2002991
200300100
2003011
2003022
2003031
2003048
2003055
2003062
2003071
2003084
2003091
20031010
2003111
2003128
2003131
2003142

FAQ

What is the Greatest Common Divisor of 200 and 300?

GCF (HCF) of 200 and 300 is 100

How to find the GCF of 200 and 300?

You can find the GCF of 200 and 300 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 200 and 300 is 100.

What prime factors do 200 and 300 share?

The prime factorizations of 200 and 300 have 2 × 2 × 5 × 5 in common, and multiplying those shared primes gives 100 — exactly the greatest common factor.

How does the GCF reduce the fraction 200/300?

Divide the numerator and the denominator by the GCF 100: 200 ÷ 100 = 2 and 300 ÷ 100 = 3. So 200/300 in lowest terms is 2/3.

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