GCF (HCF) of 21 and 84

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What is the Greatest Common Divisor of 21 and 84?

Answer

GCF (HCF) of 21 and 84 is
21

Common factors: 1, 3, 7, 21

21 divides 84 (84 ÷ 21 = 4), so the GCF is the smaller number itself.

21 = 3 × 7

84 = 22 × 3 × 7

Prime2184Lowest power
2—22—
3333
7777

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

GCF = 3 × 7 = 21

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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 84?

GCF (HCF) of 21 and 84 is 21

How to find the GCF of 21 and 84?

You can find the GCF of 21 and 84 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 21 and 84 is 21.

What prime factors do 21 and 84 share?

The prime factorizations of 21 and 84 have 3 × 7 in common, and multiplying those shared primes gives 21 — exactly the greatest common factor.

How does the GCF reduce the fraction 21/84?

Divide the numerator and the denominator by the GCF 21: 21 ÷ 21 = 1 and 84 ÷ 21 = 4. So 21/84 in lowest terms is 1/4.

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