What is the Greatest Common Factor of 25888 and 25900?

Greatest common factor (GCF) of 25888 and 25900 is 4.

GCF(25888,25900) = 4

We will now calculate the prime factors of 25888 and 25900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25888 and 25900.

How to find the GCF of 25888 and 25900?

We will first find the prime factorization of 25888 and 25900. After we will calculate the factors of 25888 and 25900 and find the biggest common factor number .

Step-1: Prime Factorization of 25888

Prime factors of 25888 are 2, 809. Prime factorization of 25888 in exponential form is:

25888 = 2⁵ × 809¹

Step-2: 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-3: Factors of 25888

List of positive integer factors of 25888 that divides 25888 without a remainder.

1, 2, 4, 8, 16, 32, 809, 1618, 3236, 6472, 12944

Step-4: Factors of 25900

List of positive integer factors of 25900 that divides 25888 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25888 and 25900. The biggest common factor number is the GCF number.
So the greatest common factor 25888 and 25900 is 4.

Also check out the Least Common Multiple of 25888 and 25900