What is the Greatest Common Factor of 38460 and 38475?

Greatest common factor (GCF) of 38460 and 38475 is 15.

GCF(38460,38475) = 15

We will now calculate the prime factors of 38460 and 38475, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38460 and 38475.

How to find the GCF of 38460 and 38475?

We will first find the prime factorization of 38460 and 38475. After we will calculate the factors of 38460 and 38475 and find the biggest common factor number .

Step-1: Prime Factorization of 38460

Prime factors of 38460 are 2, 3, 5, 641. Prime factorization of 38460 in exponential form is:

38460 = 2² × 3¹ × 5¹ × 641¹

Step-2: 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-3: Factors of 38460

List of positive integer factors of 38460 that divides 38460 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 641, 1282, 1923, 2564, 3205, 3846, 6410, 7692, 9615, 12820, 19230

Step-4: Factors of 38475

List of positive integer factors of 38475 that divides 38460 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38460 and 38475. The biggest common factor number is the GCF number.
So the greatest common factor 38460 and 38475 is 15.

Also check out the Least Common Multiple of 38460 and 38475