GCF (HCF) of 105 and 120

"Greatest Common Factor" Calculator

What is the Greatest Common Divisor of 105 and 120?

Answer

GCF (HCF) of 105 and 120 is

Common factors: 1, 3, 5, 15

15 divides both: 105 ÷ 15 = 7, 120 ÷ 15 = 8 — and 7 and 8 share no factor but 1, so no larger number divides both.

105 = 3 × 5 × 7

120 = 2³ × 3 × 5

Prime	105	120	Lowest power
2	—	2³	—
3	3	3	3
5	5	5	5
7	7	—	—

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

GCF = 3 × 5 = 15

More with these numbers

Related Calculations

GCF Table

Number 1	Number 2	GCF
105	120	15
105	126	21
105	130	5
105	140	35
105	147	21
105	150	15
105	154	7
105	165	15
105	170	5
105	175	35
105	189	21
105	195	15
105	225	15
105	245	35
105	770	35

FAQ

What is the Greatest Common Divisor of 105 and 120?

GCF (HCF) of 105 and 120 is 15

How to find the GCF of 105 and 120?

You can find the GCF of 105 and 120 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 105 and 120 is 15.

What prime factors do 105 and 120 share?

The prime factorizations of 105 and 120 have 3 × 5 in common, and multiplying those shared primes gives 15 — exactly the greatest common factor.

How does the GCF reduce the fraction 105/120?

Divide the numerator and the denominator by the GCF 15: 105 ÷ 15 = 7 and 120 ÷ 15 = 8. So 105/120 in lowest terms is 7/8.

GCF (HCF) of 105 and 120

What is the Greatest Common Divisor of 105 and 120?

More with these numbers

Related Calculations

See Also

GCF Table

FAQ

What is the Greatest Common Divisor of 105 and 120?

How to find the GCF of 105 and 120?

What prime factors do 105 and 120 share?

How does the GCF reduce the fraction 105/120?

See Also

Number 1	Number 2	GCF
105	120	15
105	126	21
105	130	5
105	140	35
105	147	21
105	150	15
105	154	7
105	165	15
105	170	5
105	175	35
105	189	21
105	195	15
105	225	15
105	245	35
105	770	35

Number 1	Number 2	GCF
105	120	15
105	126	21
105	130	5
105	140	35
105	147	21
105	150	15
105	154	7
105	165	15
105	170	5
105	175	35
105	189	21
105	195	15
105	225	15
105	245	35
105	770	35

Number 1	Number 2	GCF
105	120	15
105	126	21
105	130	5
105	140	35
105	147	21
105	150	15
105	154	7
105	165	15
105	170	5
105	175	35
105	189	21
105	195	15
105	225	15
105	245	35
105	770	35