GCF (HCF) of 84 and 105

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What is the Greatest Common Divisor of 84 and 105?

Answer

GCF (HCF) of 84 and 105 is
21

Common factors: 1, 3, 7, 21

21 divides both: 84 ÷ 21 = 4, 105 ÷ 21 = 5 — and 4 and 5 share no factor but 1, so no larger number divides both.

84 = 22 × 3 × 7

105 = 3 × 5 × 7

Prime84105Lowest power
222——
3333
5—5—
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
84906
84917
84924
84933
84942
84951
849612
84971
849814
84993
841004
841011
841026
841031
841044
8410521
841062
841071
8410812
841091
841102
841113
8411228
841131
841146
841151
841164
841173
841182
841197

FAQ

What is the Greatest Common Divisor of 84 and 105?

GCF (HCF) of 84 and 105 is 21

How to find the GCF of 84 and 105?

You can find the GCF of 84 and 105 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 84 and 105 is 21.

What prime factors do 84 and 105 share?

The prime factorizations of 84 and 105 have 3 × 7 in common, and multiplying those shared primes gives 21 — exactly the greatest common factor.

How does the GCF reduce the fraction 84/105?

Divide the numerator and the denominator by the GCF 21: 84 ÷ 21 = 4 and 105 ÷ 21 = 5. So 84/105 in lowest terms is 4/5.

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