GCF (HCF) of 100 and 105

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What is the Greatest Common Divisor of 100 and 105?

Answer

GCF (HCF) of 100 and 105 is
5

Common factors: 1, 5

5 divides both: 100 ÷ 5 = 20, 105 ÷ 5 = 21 — and 20 and 21 share no factor but 1, so no larger number divides both.

100 = 22 × 52

105 = 3 × 5 × 7

Prime100105Lowest power
222——
3—3—
55255
7—7—

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

GCF = 5

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GCF Table

Number 1Number 2GCF
100100100
1001055
10011010
10012020
1001211
10012525
1001355
10014020
1001444
1001455
10015050
10016020
1001655
10017010
10018020
1001855
10019010
100200100
1002055
10022020
10023010
1002355
10024020
1002455
10025050
10026020
10027010
10027525
10028020
10029010

FAQ

What is the Greatest Common Divisor of 100 and 105?

GCF (HCF) of 100 and 105 is 5

How to find the GCF of 100 and 105?

You can find the GCF of 100 and 105 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 100 and 105 is 5.

What prime factors do 100 and 105 share?

The prime factorizations of 100 and 105 have 5 in common, and multiplying those shared primes gives 5 — exactly the greatest common factor.

How does the GCF reduce the fraction 100/105?

Divide the numerator and the denominator by the GCF 5: 100 ÷ 5 = 20 and 105 ÷ 5 = 21. So 100/105 in lowest terms is 20/21.

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