GCF (HCF) of 100 and 420

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What is the Greatest Common Divisor of 100 and 420?

Answer

GCF (HCF) of 100 and 420 is
20

Common factors: 1, 2, 4, 5, 10, 20

20 divides both: 100 ÷ 20 = 5, 420 ÷ 20 = 21 — and 5 and 21 share no factor but 1, so no larger number divides both.

100 = 22 × 52

420 = 22 × 3 × 5 × 7

Prime100420Lowest power
2222222
3—3—
55255
7—7—

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

GCF = 22 × 5 = 20

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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 420?

GCF (HCF) of 100 and 420 is 20

How to find the GCF of 100 and 420?

You can find the GCF of 100 and 420 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 100 and 420 is 20.

What prime factors do 100 and 420 share?

The prime factorizations of 100 and 420 have 2 × 2 × 5 in common, and multiplying those shared primes gives 20 — exactly the greatest common factor.

How does the GCF reduce the fraction 100/420?

Divide the numerator and the denominator by the GCF 20: 100 ÷ 20 = 5 and 420 ÷ 20 = 21. So 100/420 in lowest terms is 5/21.

See Also