GCF (HCF) of 14 and 217

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Greatest Common Factor of
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What is the Greatest Common Divisor of 14 and 217?

Answer

GCF (HCF) of 14 and 217 is
7

Common factors: 1, 7

7 divides both: 14 ÷ 7 = 2, 217 ÷ 7 = 31 — and 2 and 31 share no factor but 1, so no larger number divides both.

14 = 2 × 7

217 = 7 × 31

Prime14217Lowest power
22——
7777
31—31—

— = 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
14271
142814
14302
14322
14331
14342
14357
14362
14371
14382
14391
14411
144214
14431
14442
14451
14462
14471
14482
14497
14502
14542
14551
145614
14582
14602
14637
148414
141057
142177

FAQ

What is the Greatest Common Divisor of 14 and 217?

GCF (HCF) of 14 and 217 is 7

How to find the GCF of 14 and 217?

You can find the GCF of 14 and 217 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 14 and 217 is 7.

What prime factors do 14 and 217 share?

The prime factorizations of 14 and 217 have 7 in common, and multiplying those shared primes gives 7 — exactly the greatest common factor.

How does the GCF reduce the fraction 14/217?

Divide the numerator and the denominator by the GCF 7: 14 ÷ 7 = 2 and 217 ÷ 7 = 31. So 14/217 in lowest terms is 2/31.

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