GCF (HCF) of 100 and 1000

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What is the Greatest Common Divisor of 100 and 1,000?

Answer

GCF (HCF) of 100 and 1,000 is
100

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

100 divides 1,000 (1,000 ÷ 100 = 10), so the GCF is the smaller number itself.

100 = 22 × 52

1,000 = 23 × 53

Prime1001,000Lowest power
2222322
5525352

GCF = 22 × 52 = 100

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GCF Table

Number 1Number 2GCF
10026020
10027010
10027525
10028020
10029010
100300100
1003055
10031010
1003155
1003355
1003455
10035050
10036020
10037010
10038020
1003955
100400100
10041010
1004155
10042020
10042525
10043010
1004355
10044020
1004455
10046020
10047010
10048020
100500100
1001,000100

FAQ

What is the Greatest Common Divisor of 100 and 1,000?

GCF (HCF) of 100 and 1,000 is 100

How to find the GCF of 100 and 1,000?

You can find the GCF of 100 and 1,000 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 100 and 1,000 is 100.

What prime factors do 100 and 1,000 share?

The prime factorizations of 100 and 1,000 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 100/1000?

Divide the numerator and the denominator by the GCF 100: 100 ÷ 100 = 1 and 1,000 ÷ 100 = 10. So 100/1000 in lowest terms is 1/10.

See Also