What is the Greatest Common Factor of 25675 and 25680?

Greatest common factor (GCF) of 25675 and 25680 is 5.

GCF(25675,25680) = 5

We will now calculate the prime factors of 25675 and 25680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25675 and 25680.

How to find the GCF of 25675 and 25680?

We will first find the prime factorization of 25675 and 25680. After we will calculate the factors of 25675 and 25680 and find the biggest common factor number .

Step-1: Prime Factorization of 25675

Prime factors of 25675 are 5, 13, 79. Prime factorization of 25675 in exponential form is:

25675 = 5² × 13¹ × 79¹

Step-2: Prime Factorization of 25680

Prime factors of 25680 are 2, 3, 5, 107. Prime factorization of 25680 in exponential form is:

25680 = 2⁴ × 3¹ × 5¹ × 107¹

Step-3: Factors of 25675

List of positive integer factors of 25675 that divides 25675 without a remainder.

1, 5, 13, 25, 65, 79, 325, 395, 1027, 1975, 5135

Step-4: Factors of 25680

List of positive integer factors of 25680 that divides 25675 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 107, 120, 214, 240, 321, 428, 535, 642, 856, 1070, 1284, 1605, 1712, 2140, 2568, 3210, 4280, 5136, 6420, 8560, 12840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25675 and 25680. The biggest common factor number is the GCF number.
So the greatest common factor 25675 and 25680 is 5.

Also check out the Least Common Multiple of 25675 and 25680