What is the Greatest Common Factor of 460 and 475?

Greatest common factor (GCF) of 460 and 475 is 5.

GCF(460,475) = 5

We will now calculate the prime factors of 460 and 475, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 460 and 475.

How to find the GCF of 460 and 475?

We will first find the prime factorization of 460 and 475. After we will calculate the factors of 460 and 475 and find the biggest common factor number .

Step-1: Prime Factorization of 460

Prime factors of 460 are 2, 5, 23. Prime factorization of 460 in exponential form is:

460 = 2² × 5¹ × 23¹

Step-2: Prime Factorization of 475

Prime factors of 475 are 5, 19. Prime factorization of 475 in exponential form is:

475 = 5² × 19¹

Step-3: Factors of 460

List of positive integer factors of 460 that divides 460 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230

Step-4: Factors of 475

List of positive integer factors of 475 that divides 460 without a remainder.

1, 5, 19, 25, 95

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 460 and 475. The biggest common factor number is the GCF number.
So the greatest common factor 460 and 475 is 5.

Also check out the Least Common Multiple of 460 and 475