GCF of 105 and 120 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 105 and 120?

Answer

GCF of 105 and 120 is
15

(Fifteen)

Finding GCF for 105 and 120 using all factors (divisors) listing

The first method to find GCF for numbers 105 and 120 is to list all factors for both numbers and pick the highest common one:

All factors of 105: 1, 3, 5, 7, 15, 21, 35, 105

All factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

So the Greatest Common Factor for 105 and 120 is 15

Finding GCF for 105 and 120 by Prime Factorization

The second method to find GCF for numbers 105 and 120 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 105: 3, 5, 7

All Prime Factors of 120: 2, 2, 2, 3, 5

As we can see there are Prime Factors common to both numbers: 3, 5

Now we need to multiply them to find GCF: 3 × 5 = 15

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About "Greatest Common Factor" Calculator

This calculator will help you find the greatest common factor (GCF) of two numbers. For example, it can help you find out what is the Greatest Common Divisor of 105 and 120? (The answer is: 15). Select the first number (e.g. '105') and the second number (e.g. '120'). After that hit the 'Calculate' button.
Greatest Common Factor (GCF) also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) - it is the largest positive integer that divides each of the integers with zero remainder.
"Greatest Common Factor" Calculator
Greatest Common Factor of
and

GCF Table

Number 1Number 2GCF
10512015
10512621
1051305
10514035
10514721
10515015
1051547
10516515
1051705
10517535
10518921
10519515
10522515
10524535
10577035

FAQ

What is the Greatest Common Divisor of 105 and 120?

GCF 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.

See Also