What is the Greatest Common Factor of 25900 and 25920?

Greatest common factor (GCF) of 25900 and 25920 is 20.

GCF(25900,25920) = 20

We will now calculate the prime factors of 25900 and 25920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25900 and 25920.

How to find the GCF of 25900 and 25920?

We will first find the prime factorization of 25900 and 25920. After we will calculate the factors of 25900 and 25920 and find the biggest common factor number .

Step-1: Prime Factorization of 25900

Prime factors of 25900 are 2, 5, 7, 37. Prime factorization of 25900 in exponential form is:

25900 = 2² × 5² × 7¹ × 37¹

Step-2: 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-3: Factors of 25900

List of positive integer factors of 25900 that divides 25900 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 37, 50, 70, 74, 100, 140, 148, 175, 185, 259, 350, 370, 518, 700, 740, 925, 1036, 1295, 1850, 2590, 3700, 5180, 6475, 12950

Step-4: Factors of 25920

List of positive integer factors of 25920 that divides 25900 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25900 and 25920. The biggest common factor number is the GCF number.
So the greatest common factor 25900 and 25920 is 20.

Also check out the Least Common Multiple of 25900 and 25920