What is the Greatest Common Factor of 10900 and 10906?

Greatest common factor (GCF) of 10900 and 10906 is 2.

GCF(10900,10906) = 2

We will now calculate the prime factors of 10900 and 10906, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10900 and 10906.

How to find the GCF of 10900 and 10906?

We will first find the prime factorization of 10900 and 10906. After we will calculate the factors of 10900 and 10906 and find the biggest common factor number .

Step-1: Prime Factorization of 10900

Prime factors of 10900 are 2, 5, 109. Prime factorization of 10900 in exponential form is:

10900 = 2² × 5² × 109¹

Step-2: 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-3: Factors of 10900

List of positive integer factors of 10900 that divides 10900 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 109, 218, 436, 545, 1090, 2180, 2725, 5450

Step-4: Factors of 10906

List of positive integer factors of 10906 that divides 10900 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10900 and 10906. The biggest common factor number is the GCF number.
So the greatest common factor 10900 and 10906 is 2.

Also check out the Least Common Multiple of 10900 and 10906