What is the Greatest Common Factor of 10900 and 10914?

Greatest common factor (GCF) of 10900 and 10914 is 2.

GCF(10900,10914) = 2

We will now calculate the prime factors of 10900 and 10914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10900 and 10914.

How to find the GCF of 10900 and 10914?

We will first find the prime factorization of 10900 and 10914. After we will calculate the factors of 10900 and 10914 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 10914

Prime factors of 10914 are 2, 3, 17, 107. Prime factorization of 10914 in exponential form is:

10914 = 2¹ × 3¹ × 17¹ × 107¹

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 10914

List of positive integer factors of 10914 that divides 10900 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 107, 214, 321, 642, 1819, 3638, 5457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10900 and 10914. The biggest common factor number is the GCF number.
So the greatest common factor 10900 and 10914 is 2.

Also check out the Least Common Multiple of 10900 and 10914