What is the Greatest Common Factor of 25100 and 25114?

Greatest common factor (GCF) of 25100 and 25114 is 2.

GCF(25100,25114) = 2

We will now calculate the prime factors of 25100 and 25114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25100 and 25114.

How to find the GCF of 25100 and 25114?

We will first find the prime factorization of 25100 and 25114. After we will calculate the factors of 25100 and 25114 and find the biggest common factor number .

Step-1: Prime Factorization of 25100

Prime factors of 25100 are 2, 5, 251. Prime factorization of 25100 in exponential form is:

25100 = 2² × 5² × 251¹

Step-2: Prime Factorization of 25114

Prime factors of 25114 are 2, 29, 433. Prime factorization of 25114 in exponential form is:

25114 = 2¹ × 29¹ × 433¹

Step-3: Factors of 25100

List of positive integer factors of 25100 that divides 25100 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 251, 502, 1004, 1255, 2510, 5020, 6275, 12550

Step-4: Factors of 25114

List of positive integer factors of 25114 that divides 25100 without a remainder.

1, 2, 29, 58, 433, 866, 12557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25100 and 25114. The biggest common factor number is the GCF number.
So the greatest common factor 25100 and 25114 is 2.

Also check out the Least Common Multiple of 25100 and 25114