What is the greatest common factor of 25 and 55?

Answer 1

The GCF of 25 and 55 is 5.

The factors of 25 are 1, 5, and 25. The factors of 55 are 1, 5, 11, and 55. So the GCF of 25 and 55 is 5

The greatest common factor of two or more numbers is the greatest common divisor of all of them, meaning it's the largest positive integer that divides the numbers without remainders. One way to find the GCF is to use prime factorization. Rewrite each number as a product of all prime numbers. Then find the primes that the numbers have in common, multiply those factors together, and you have your GCF! In this example:

25

Start with 2, the first prime. Doesn't divide evenly. So go to next prime, 3. Same thing. Go to next prime, 5. 25 = 5 x 5. Both factors are prime, so you can't go any further with that one.

55

Again, start with 2. No go. Try 3. Nope. Try 5. 55 = 5 x 11. Both factors are prime. You've gone as far as you can go.

What prime factors do these two numbers have in common? Just a 5! So 5 is the GCF of 25 and 55.
The GCF of 25 and 55 is 5.