GCF (HCF) of 14 and 21

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Greatest Common Factor of
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What is the Greatest Common Divisor of 14 and 21?

Answer

GCF (HCF) of 14 and 21 is
7

Common factors: 1, 7

7 divides both: 14 ÷ 7 = 2, 21 ÷ 7 = 3 — and 2 and 3 share no factor but 1, so no larger number divides both.

14 = 2 × 7

21 = 3 × 7

Prime1421Lowest power
22——
3—3—
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
1411
1491
14151
14162
14171
14182
14191
14202
14217
14222
14231
14242
14251
14262
14271
142814
14302
14322
14331
14342
14357
14362
14382
14391
14411
144214
14431
14442
14451
14462

FAQ

What is the Greatest Common Divisor of 14 and 21?

GCF (HCF) of 14 and 21 is 7

How to find the GCF of 14 and 21?

You can find the GCF of 14 and 21 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 14 and 21 is 7.

What prime factors do 14 and 21 share?

The prime factorizations of 14 and 21 have 7 in common, and multiplying those shared primes gives 7 — exactly the greatest common factor.

How does the GCF reduce the fraction 14/21?

Divide the numerator and the denominator by the GCF 7: 14 ÷ 7 = 2 and 21 ÷ 7 = 3. So 14/21 in lowest terms is 2/3.

See Also