GCF (HCF) of 120 and 168

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What is the Greatest Common Divisor of 120 and 168?

Answer

GCF (HCF) of 120 and 168 is
24

Common factors: 1, 2, 3, 4, 6, 8, 12, 24

24 divides both: 120 ÷ 24 = 5, 168 ÷ 24 = 7 — and 5 and 7 share no factor but 1, so no larger number divides both.

120 = 23 × 3 × 5

168 = 23 × 3 × 7

Prime120168Lowest power
2232323
3333
55——
7—7—

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

GCF = 23 × 3 = 24

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GCF Table

Number 1Number 2GCF
1201533
1201542
1201555
12015612
1201571
1201582
1201593
12016040
1201611
1201626
1201631
1201644
12016515
1201662
1201671
12016824
1201691
12017010
1201713
1201724
1201731
1201746
1201755
1201768
1201773
1201782
1201791
12018060
1201811
1201822

FAQ

What is the Greatest Common Divisor of 120 and 168?

GCF (HCF) of 120 and 168 is 24

How to find the GCF of 120 and 168?

You can find the GCF of 120 and 168 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 120 and 168 is 24.

What prime factors do 120 and 168 share?

The prime factorizations of 120 and 168 have 2 × 2 × 2 × 3 in common, and multiplying those shared primes gives 24 — exactly the greatest common factor.

How does the GCF reduce the fraction 120/168?

Divide the numerator and the denominator by the GCF 24: 120 ÷ 24 = 5 and 168 ÷ 24 = 7. So 120/168 in lowest terms is 5/7.

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