GCF (HCF) of 200 and 500

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What is the Greatest Common Divisor of 200 and 500?

Answer

GCF (HCF) of 200 and 500 is
100

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

100 divides both: 200 ÷ 100 = 2, 500 ÷ 100 = 5 — and 2 and 5 share no factor but 1, so no larger number divides both.

200 = 23 × 52

500 = 22 × 53

Prime200500Lowest power
2232222
5525352

GCF = 22 × 52 = 100

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GCF Table

Number 1Number 2GCF
2004855
2004862
2004871
2004888
2004891
20049010
2004911
2004924
2004931
2004942
2004955
2004968
2004971
2004982
2004991
200500100
2005011
2005022
2005031
2005048
2005055
2005062
2005071
2005084
2005091
20051010
2005111
2005128
2005131
2005142

FAQ

What is the Greatest Common Divisor of 200 and 500?

GCF (HCF) of 200 and 500 is 100

How to find the GCF of 200 and 500?

You can find the GCF of 200 and 500 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 200 and 500 is 100.

What prime factors do 200 and 500 share?

The prime factorizations of 200 and 500 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 200/500?

Divide the numerator and the denominator by the GCF 100: 200 ÷ 100 = 2 and 500 ÷ 100 = 5. So 200/500 in lowest terms is 2/5.

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