What is the Greatest Common Factor of 25920 and 25935?

Greatest common factor (GCF) of 25920 and 25935 is 15.

GCF(25920,25935) = 15

We will now calculate the prime factors of 25920 and 25935, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25920 and 25935.

How to find the GCF of 25920 and 25935?

We will first find the prime factorization of 25920 and 25935. After we will calculate the factors of 25920 and 25935 and find the biggest common factor number .

Step-1: Prime Factorization of 25920

Prime factors of 25920 are 2, 3, 5. Prime factorization of 25920 in exponential form is:

25920 = 2⁶ × 3⁴ × 5¹

Step-2: Prime Factorization of 25935

Prime factors of 25935 are 3, 5, 7, 13, 19. Prime factorization of 25935 in exponential form is:

25935 = 3¹ × 5¹ × 7¹ × 13¹ × 19¹

Step-3: Factors of 25920

List of positive integer factors of 25920 that divides 25920 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 81, 90, 96, 108, 120, 135, 144, 160, 162, 180, 192, 216, 240, 270, 288, 320, 324, 360, 405, 432, 480, 540, 576, 648, 720, 810, 864, 960, 1080, 1296, 1440, 1620, 1728, 2160, 2592, 2880, 3240, 4320, 5184, 6480, 8640, 12960

Step-4: Factors of 25935

List of positive integer factors of 25935 that divides 25920 without a remainder.

1, 3, 5, 7, 13, 15, 19, 21, 35, 39, 57, 65, 91, 95, 105, 133, 195, 247, 273, 285, 399, 455, 665, 741, 1235, 1365, 1729, 1995, 3705, 5187, 8645

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25920 and 25935. The biggest common factor number is the GCF number.
So the greatest common factor 25920 and 25935 is 15.

Also check out the Least Common Multiple of 25920 and 25935