What is the Greatest Common Factor of 10906 and 10925?

Greatest common factor (GCF) of 10906 and 10925 is 19.

GCF(10906,10925) = 19

We will now calculate the prime factors of 10906 and 10925, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10906 and 10925.

How to find the GCF of 10906 and 10925?

We will first find the prime factorization of 10906 and 10925. After we will calculate the factors of 10906 and 10925 and find the biggest common factor number .

Step-1: Prime Factorization of 10906

Prime factors of 10906 are 2, 7, 19, 41. Prime factorization of 10906 in exponential form is:

10906 = 2¹ × 7¹ × 19¹ × 41¹

Step-2: Prime Factorization of 10925

Prime factors of 10925 are 5, 19, 23. Prime factorization of 10925 in exponential form is:

10925 = 5² × 19¹ × 23¹

Step-3: Factors of 10906

List of positive integer factors of 10906 that divides 10906 without a remainder.

1, 2, 7, 14, 19, 38, 41, 82, 133, 266, 287, 574, 779, 1558, 5453

Step-4: Factors of 10925

List of positive integer factors of 10925 that divides 10906 without a remainder.

1, 5, 19, 23, 25, 95, 115, 437, 475, 575, 2185

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10906 and 10925. The biggest common factor number is the GCF number.
So the greatest common factor 10906 and 10925 is 19.

Also check out the Least Common Multiple of 10906 and 10925