GCF (HCF) of 28 and 105

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What is the Greatest Common Divisor of 28 and 105?

Answer

GCF (HCF) of 28 and 105 is
7

Common factors: 1, 7

7 divides both: 28 ÷ 7 = 4, 105 ÷ 7 = 15 — and 4 and 15 share no factor but 1, so no larger number divides both.

28 = 22 × 7

105 = 3 × 5 × 7

Prime28105Lowest power
222——
3—3—
5—5—
7777

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

GCF = 7

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GCF Table

Number 1Number 2GCF
28302
28311
28324
28342
28357
28364
28382
28391
28404
284214
28431
28444
28451
28462
28484
28497
28502
28531
28551
285628
28604
28637
28644
287014
28724
28804
288428
289814
281057
2812614

FAQ

What is the Greatest Common Divisor of 28 and 105?

GCF (HCF) of 28 and 105 is 7

How to find the GCF of 28 and 105?

You can find the GCF of 28 and 105 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 28 and 105 is 7.

What prime factors do 28 and 105 share?

The prime factorizations of 28 and 105 have 7 in common, and multiplying those shared primes gives 7 — exactly the greatest common factor.

How does the GCF reduce the fraction 28/105?

Divide the numerator and the denominator by the GCF 7: 28 ÷ 7 = 4 and 105 ÷ 7 = 15. So 28/105 in lowest terms is 4/15.

See Also