What is the Greatest Common Factor of 38265 and 38280?

Greatest common factor (GCF) of 38265 and 38280 is 15.

GCF(38265,38280) = 15

We will now calculate the prime factors of 38265 and 38280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38265 and 38280.

How to find the GCF of 38265 and 38280?

We will first find the prime factorization of 38265 and 38280. After we will calculate the factors of 38265 and 38280 and find the biggest common factor number .

Step-1: Prime Factorization of 38265

Prime factors of 38265 are 3, 5, 2551. Prime factorization of 38265 in exponential form is:

38265 = 3¹ × 5¹ × 2551¹

Step-2: Prime Factorization of 38280

Prime factors of 38280 are 2, 3, 5, 11, 29. Prime factorization of 38280 in exponential form is:

38280 = 2³ × 3¹ × 5¹ × 11¹ × 29¹

Step-3: Factors of 38265

List of positive integer factors of 38265 that divides 38265 without a remainder.

1, 3, 5, 15, 2551, 7653, 12755

Step-4: Factors of 38280

List of positive integer factors of 38280 that divides 38265 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 29, 30, 33, 40, 44, 55, 58, 60, 66, 87, 88, 110, 116, 120, 132, 145, 165, 174, 220, 232, 264, 290, 319, 330, 348, 435, 440, 580, 638, 660, 696, 870, 957, 1160, 1276, 1320, 1595, 1740, 1914, 2552, 3190, 3480, 3828, 4785, 6380, 7656, 9570, 12760, 19140

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38265 and 38280. The biggest common factor number is the GCF number.
So the greatest common factor 38265 and 38280 is 15.

Also check out the Least Common Multiple of 38265 and 38280