GCF (HCF) of 30 and 51

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Greatest Common Factor of
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What is the Greatest Common Divisor of 30 and 51?

Answer

GCF (HCF) of 30 and 51 is
3

Common factors: 1, 3

3 divides both: 30 ÷ 3 = 10, 51 ÷ 3 = 17 — and 10 and 17 share no factor but 1, so no larger number divides both.

30 = 2 × 3 × 5

51 = 3 × 17

Prime3051Lowest power
22——
3333
55——
17—17—

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

GCF = 3

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GCF Table

Number 1Number 2GCF
30322
30342
30355
30366
30382
30393
304010
30426
30431
30442
304515
30486
30491
305010
30513
30522
30531
30546
30555
30562
30582
306030
307010
307515
308010
30966
3010010
3010515
3011010
301155

FAQ

What is the Greatest Common Divisor of 30 and 51?

GCF (HCF) of 30 and 51 is 3

How to find the GCF of 30 and 51?

You can find the GCF of 30 and 51 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 30 and 51 is 3.

What prime factors do 30 and 51 share?

The prime factorizations of 30 and 51 have 3 in common, and multiplying those shared primes gives 3 — exactly the greatest common factor.

How does the GCF reduce the fraction 30/51?

Divide the numerator and the denominator by the GCF 3: 30 ÷ 3 = 10 and 51 ÷ 3 = 17. So 30/51 in lowest terms is 10/17.

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