GCF (HCF) of 30 and 100

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What is the Greatest Common Divisor of 30 and 100?

Answer

GCF (HCF) of 30 and 100 is
10

Common factors: 1, 2, 5, 10

10 divides both: 30 ÷ 10 = 3, 100 ÷ 10 = 10 — and 3 and 10 share no factor but 1, so no larger number divides both.

30 = 2 × 3 × 5

100 = 22 × 52

Prime30100Lowest power
22222
33——
55525

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

GCF = 2 × 5 = 10

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GCF Table

Number 1Number 2GCF
30486
30491
305010
30513
30522
30531
30546
30555
30562
30582
306030
307010
307515
308010
30966
3010010
3010515
3011010
301155
3012030
3013010
3013515
3015030
3017010
3019515
3021030
302382
3029010
303055
3033030

FAQ

What is the Greatest Common Divisor of 30 and 100?

GCF (HCF) of 30 and 100 is 10

How to find the GCF of 30 and 100?

You can find the GCF of 30 and 100 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 30 and 100 is 10.

What prime factors do 30 and 100 share?

The prime factorizations of 30 and 100 have 2 × 5 in common, and multiplying those shared primes gives 10 — exactly the greatest common factor.

How does the GCF reduce the fraction 30/100?

Divide the numerator and the denominator by the GCF 10: 30 ÷ 10 = 3 and 100 ÷ 10 = 10. So 30/100 in lowest terms is 3/10.

See Also