What is the Greatest Common Factor of 25690 and 25700?

Greatest common factor (GCF) of 25690 and 25700 is 10.

GCF(25690,25700) = 10

We will now calculate the prime factors of 25690 and 25700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25690 and 25700.

How to find the GCF of 25690 and 25700?

We will first find the prime factorization of 25690 and 25700. After we will calculate the factors of 25690 and 25700 and find the biggest common factor number .

Step-1: Prime Factorization of 25690

Prime factors of 25690 are 2, 5, 7, 367. Prime factorization of 25690 in exponential form is:

25690 = 2¹ × 5¹ × 7¹ × 367¹

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 25690

List of positive integer factors of 25690 that divides 25690 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 367, 734, 1835, 2569, 3670, 5138, 12845

Step-4: Factors of 25700

List of positive integer factors of 25700 that divides 25690 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 25690 and 25700. The biggest common factor number is the GCF number.
So the greatest common factor 25690 and 25700 is 10.

Also check out the Least Common Multiple of 25690 and 25700