What is the Greatest Common Factor of 10900 and 10912?

Greatest common factor (GCF) of 10900 and 10912 is 4.

GCF(10900,10912) = 4

We will now calculate the prime factors of 10900 and 10912, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10900 and 10912.

How to find the GCF of 10900 and 10912?

We will first find the prime factorization of 10900 and 10912. After we will calculate the factors of 10900 and 10912 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 10912

Prime factors of 10912 are 2, 11, 31. Prime factorization of 10912 in exponential form is:

10912 = 2⁵ × 11¹ × 31¹

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 10912

List of positive integer factors of 10912 that divides 10900 without a remainder.

1, 2, 4, 8, 11, 16, 22, 31, 32, 44, 62, 88, 124, 176, 248, 341, 352, 496, 682, 992, 1364, 2728, 5456

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10900 and 10912. The biggest common factor number is the GCF number.
So the greatest common factor 10900 and 10912 is 4.

Also check out the Least Common Multiple of 10900 and 10912