What is the Greatest Common Factor of 38475 and 38480?

Greatest common factor (GCF) of 38475 and 38480 is 5.

GCF(38475,38480) = 5

We will now calculate the prime factors of 38475 and 38480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38475 and 38480.

How to find the GCF of 38475 and 38480?

We will first find the prime factorization of 38475 and 38480. After we will calculate the factors of 38475 and 38480 and find the biggest common factor number .

Step-1: Prime Factorization of 38475

Prime factors of 38475 are 3, 5, 19. Prime factorization of 38475 in exponential form is:

38475 = 3⁴ × 5² × 19¹

Step-2: Prime Factorization of 38480

Prime factors of 38480 are 2, 5, 13, 37. Prime factorization of 38480 in exponential form is:

38480 = 2⁴ × 5¹ × 13¹ × 37¹

Step-3: Factors of 38475

List of positive integer factors of 38475 that divides 38475 without a remainder.

1, 3, 5, 9, 15, 19, 25, 27, 45, 57, 75, 81, 95, 135, 171, 225, 285, 405, 475, 513, 675, 855, 1425, 1539, 2025, 2565, 4275, 7695, 12825

Step-4: Factors of 38480

List of positive integer factors of 38480 that divides 38475 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 37, 40, 52, 65, 74, 80, 104, 130, 148, 185, 208, 260, 296, 370, 481, 520, 592, 740, 962, 1040, 1480, 1924, 2405, 2960, 3848, 4810, 7696, 9620, 19240

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38475 and 38480. The biggest common factor number is the GCF number.
So the greatest common factor 38475 and 38480 is 5.

Also check out the Least Common Multiple of 38475 and 38480