GCF (HCF) of 30 and 130

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What is the Greatest Common Divisor of 30 and 130?

Answer

GCF (HCF) of 30 and 130 is
10

Common factors: 1, 2, 5, 10

10 divides both: 30 ÷ 10 = 3, 130 ÷ 10 = 13 — and 3 and 13 share no factor but 1, so no larger number divides both.

30 = 2 × 3 × 5

130 = 2 × 5 × 13

Prime30130Lowest power
2222
33——
5555
13—13—

— = 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
30531
30546
30555
30562
30582
306030
307010
307515
308010
30966
3010010
3010515
3011010
301155
3012030
3013010
3013515
3015030
3016515
3017010
3018030
3019515
3021030
302355
302382
3029010
303055
3033030
3034010
3035010

FAQ

What is the Greatest Common Divisor of 30 and 130?

GCF (HCF) of 30 and 130 is 10

How to find the GCF of 30 and 130?

You can find the GCF of 30 and 130 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 30 and 130 is 10.

What prime factors do 30 and 130 share?

The prime factorizations of 30 and 130 have 2 × 5 in common, and multiplying those shared primes gives 10 — exactly the greatest common factor.

How does the GCF reduce the fraction 30/130?

Divide the numerator and the denominator by the GCF 10: 30 ÷ 10 = 3 and 130 ÷ 10 = 13. So 30/130 in lowest terms is 3/13.

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