GCF (HCF) of 21 and 45

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Greatest Common Factor of
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What is the Greatest Common Divisor of 21 and 45?

Answer

GCF (HCF) of 21 and 45 is
3

Common factors: 1, 3

3 divides both: 21 ÷ 3 = 7, 45 ÷ 3 = 15 — and 7 and 15 share no factor but 1, so no larger number divides both.

21 = 3 × 7

45 = 32 × 5

Prime2145Lowest power
33323
5—5—
77——

— = 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
21221
21243
21251
21261
21273
21287
21303
21321
21333
21357
21363
21371
21381
21393
21401
214221
21441
21453
21461
21483
21497
21501
21513
21543
21567
21603
21693
21801
218421
2110521

FAQ

What is the Greatest Common Divisor of 21 and 45?

GCF (HCF) of 21 and 45 is 3

How to find the GCF of 21 and 45?

You can find the GCF of 21 and 45 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 21 and 45 is 3.

What prime factors do 21 and 45 share?

The prime factorizations of 21 and 45 have 3 in common, and multiplying those shared primes gives 3 — exactly the greatest common factor.

How does the GCF reduce the fraction 21/45?

Divide the numerator and the denominator by the GCF 3: 21 ÷ 3 = 7 and 45 ÷ 3 = 15. So 21/45 in lowest terms is 7/15.

See Also