GCF (HCF) of 30 and 120

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What is the Greatest Common Divisor of 30 and 120?

Answer

GCF (HCF) of 30 and 120 is
30

Common factors: 1, 2, 3, 5, 6, 10, 15, 30

30 divides 120 (120 ÷ 30 = 4), so the GCF is the smaller number itself.

30 = 2 × 3 × 5

120 = 23 × 3 × 5

Prime30120Lowest power
22232
3333
5555

GCF = 2 × 3 × 5 = 30

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GCF Table

Number 1Number 2GCF
30522
30531
30546
30555
30562
30582
306030
307010
307515
308010
30966
3010010
3010515
3011010
301155
3012030
3013010
3013515
3015030
3017010
3019515
302355
302382
3029010
303055
3033030
3034010
3035010
3040515
304155

FAQ

What is the Greatest Common Divisor of 30 and 120?

GCF (HCF) of 30 and 120 is 30

How to find the GCF of 30 and 120?

You can find the GCF of 30 and 120 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 30 and 120 is 30.

What prime factors do 30 and 120 share?

The prime factorizations of 30 and 120 have 2 × 3 × 5 in common, and multiplying those shared primes gives 30 — exactly the greatest common factor.

How does the GCF reduce the fraction 30/120?

Divide the numerator and the denominator by the GCF 30: 30 ÷ 30 = 1 and 120 ÷ 30 = 4. So 30/120 in lowest terms is 1/4.

See Also