GCF of 75 and 105 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 75 and 105?

Answer

GCF of 75 and 105 is
15

(Fifteen)

Finding GCF for 75 and 105 using all factors (divisors) listing

The first method to find GCF for numbers 75 and 105 is to list all factors for both numbers and pick the highest common one:

All factors of 75: 1, 3, 5, 15, 25, 75

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

So the Greatest Common Factor for 75 and 105 is 15

Finding GCF for 75 and 105 by Prime Factorization

The second method to find GCF for numbers 75 and 105 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 75: 3, 5, 5

All Prime Factors of 105: 3, 5, 7

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 75 and 105? (The answer is: 15). Select the first number (e.g. '75') and the second number (e.g. '105'). 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
759015
75911
75921
75933
75941
75955
75963
75971
75981
75993
7510025
751011
751023
751031
751041
7510515
751061
751071
751083
751091
751105
751113
751121
751131
751143
751155
751161
751173
751181
751191

FAQ

What is the Greatest Common Divisor of 75 and 105?

GCF of 75 and 105 is 15

How to find the GCF of 75 and 105?

You can find the GCF of 75 and 105 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 75 and 105 is 15.

What prime factors do 75 and 105 share?

The prime factorizations of 75 and 105 have 3 × 5 in common, and multiplying those shared primes gives 15 — exactly the greatest common factor.

How does the GCF reduce the fraction 75/105?

Divide the numerator and the denominator by the GCF 15: 75 ÷ 15 = 5 and 105 ÷ 15 = 7. So 75/105 in lowest terms is 5/7.

See Also