GCF (HCF) of 14 and 84

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What is the Greatest Common Divisor of 14 and 84?

Answer

GCF (HCF) of 14 and 84 is
14

Common factors: 1, 2, 7, 14

14 divides 84 (84 ÷ 14 = 6), so the GCF is the smaller number itself.

14 = 2 × 7

84 = 22 × 3 × 7

Prime1484Lowest power
22222
3—3—
7777

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

GCF = 2 × 7 = 14

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GCF Table

Number 1Number 2GCF
14262
14271
142814
14302
14322
14331
14342
14357
14362
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 84?

GCF (HCF) of 14 and 84 is 14

How to find the GCF of 14 and 84?

You can find the GCF of 14 and 84 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 14 and 84 is 14.

What prime factors do 14 and 84 share?

The prime factorizations of 14 and 84 have 2 × 7 in common, and multiplying those shared primes gives 14 — exactly the greatest common factor.

How does the GCF reduce the fraction 14/84?

Divide the numerator and the denominator by the GCF 14: 14 ÷ 14 = 1 and 84 ÷ 14 = 6. So 14/84 in lowest terms is 1/6.

See Also