What is the Greatest Common Factor of 17475 and 17480?

Greatest common factor (GCF) of 17475 and 17480 is 5.

GCF(17475,17480) = 5

We will now calculate the prime factors of 17475 and 17480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17475 and 17480.

How to find the GCF of 17475 and 17480?

We will first find the prime factorization of 17475 and 17480. After we will calculate the factors of 17475 and 17480 and find the biggest common factor number .

Step-1: Prime Factorization of 17475

Prime factors of 17475 are 3, 5, 233. Prime factorization of 17475 in exponential form is:

17475 = 3¹ × 5² × 233¹

Step-2: Prime Factorization of 17480

Prime factors of 17480 are 2, 5, 19, 23. Prime factorization of 17480 in exponential form is:

17480 = 2³ × 5¹ × 19¹ × 23¹

Step-3: Factors of 17475

List of positive integer factors of 17475 that divides 17475 without a remainder.

1, 3, 5, 15, 25, 75, 233, 699, 1165, 3495, 5825

Step-4: Factors of 17480

List of positive integer factors of 17480 that divides 17475 without a remainder.

1, 2, 4, 5, 8, 10, 19, 20, 23, 38, 40, 46, 76, 92, 95, 115, 152, 184, 190, 230, 380, 437, 460, 760, 874, 920, 1748, 2185, 3496, 4370, 8740

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17475 and 17480. The biggest common factor number is the GCF number.
So the greatest common factor 17475 and 17480 is 5.

Also check out the Least Common Multiple of 17475 and 17480