GCF (HCF) of 120 and 144

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What is the Greatest Common Divisor of 120 and 144?

Answer

GCF (HCF) of 120 and 144 is
24

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

24 divides both: 120 ÷ 24 = 5, 144 ÷ 24 = 6 — and 5 and 6 share no factor but 1, so no larger number divides both.

120 = 23 × 3 × 5

144 = 24 × 32

Prime120144Lowest power
2232423
33323
55——

— = 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
1201293
12013010
1201311
12013212
1201331
1201342
12013515
1201368
1201371
1201386
1201391
12014020
1201413
1201422
1201431
12014424
1201455
1201462
1201473
1201484
1201491
12015030
1201511
1201528
1201533
1201542
1201555
12015612
1201571
1201582

FAQ

What is the Greatest Common Divisor of 120 and 144?

GCF (HCF) of 120 and 144 is 24

How to find the GCF of 120 and 144?

You can find the GCF of 120 and 144 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 120 and 144 is 24.

What prime factors do 120 and 144 share?

The prime factorizations of 120 and 144 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 120/144?

Divide the numerator and the denominator by the GCF 24: 120 ÷ 24 = 5 and 144 ÷ 24 = 6. So 120/144 in lowest terms is 5/6.

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