GCF of 25 and 105 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 25 and 105?

Answer

GCF of 25 and 105 is
5

(Five)

Finding GCF for 25 and 105 using all factors (divisors) listing

The first method to find GCF for numbers 25 and 105 is to list all factors for both numbers and pick the highest common one:

All factors of 25: 1, 5, 25

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

So the Greatest Common Factor for 25 and 105 is 5

Finding GCF for 25 and 105 by Prime Factorization

The second method to find GCF for numbers 25 and 105 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 25: 5, 5

All Prime Factors of 105: 3, 5, 7

As we can see there is only one Prime Factor common to both numbers. It is 5

So 5 is the Greatest Common Factor of 25 and 105

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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 25 and 105? (The answer is: 5). Select the first number (e.g. '25') 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
25331
25355
25361
25391
25405
25421
25441
25455
25481
25491
255025
25521
25555
25561
25605
25641
25655
25705
257525
25805
25811
25905
2510025
251055
251211
2512525
251441
2515025
2517525
2520025

FAQ

What is the Greatest Common Divisor of 25 and 105?

GCF of 25 and 105 is 5

How to find the GCF of 25 and 105?

You can find the GCF of 25 and 105 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 25 and 105 is 5.

What prime factors do 25 and 105 share?

The prime factorizations of 25 and 105 have 5 in common, and multiplying those shared primes gives 5 — exactly the greatest common factor.

How does the GCF reduce the fraction 25/105?

Divide the numerator and the denominator by the GCF 5: 25 ÷ 5 = 5 and 105 ÷ 5 = 21. So 25/105 in lowest terms is 5/21.

See Also