What is the Greatest Common Factor of 25680 and 25700?

Greatest common factor (GCF) of 25680 and 25700 is 20.

GCF(25680,25700) = 20

We will now calculate the prime factors of 25680 and 25700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25680 and 25700.

How to find the GCF of 25680 and 25700?

We will first find the prime factorization of 25680 and 25700. After we will calculate the factors of 25680 and 25700 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 25700

Prime factors of 25700 are 2, 5, 257. Prime factorization of 25700 in exponential form is:

25700 = 2² × 5² × 257¹

Step-3: Factors of 25680

List of positive integer factors of 25680 that divides 25680 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

Step-4: Factors of 25700

List of positive integer factors of 25700 that divides 25680 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 257, 514, 1028, 1285, 2570, 5140, 6425, 12850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25680 and 25700. The biggest common factor number is the GCF number.
So the greatest common factor 25680 and 25700 is 20.

Also check out the Least Common Multiple of 25680 and 25700