What is the Greatest Common Factor of 475 and 480?

Greatest common factor (GCF) of 475 and 480 is 5.

GCF(475,480) = 5

We will now calculate the prime factors of 475 and 480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 475 and 480.

How to find the GCF of 475 and 480?

We will first find the prime factorization of 475 and 480. After we will calculate the factors of 475 and 480 and find the biggest common factor number .

Step-1: Prime Factorization of 475

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

475 = 5² × 19¹

Step-2: Prime Factorization of 480

Prime factors of 480 are 2, 3, 5. Prime factorization of 480 in exponential form is:

480 = 2⁵ × 3¹ × 5¹

Step-3: Factors of 475

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

1, 5, 19, 25, 95

Step-4: Factors of 480

List of positive integer factors of 480 that divides 475 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 475 and 480. The biggest common factor number is the GCF number.
So the greatest common factor 475 and 480 is 5.

Also check out the Least Common Multiple of 475 and 480