What is the Greatest Common Factor of 22900 and 22914?

Greatest common factor (GCF) of 22900 and 22914 is 2.

GCF(22900,22914) = 2

We will now calculate the prime factors of 22900 and 22914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22900 and 22914.

How to find the GCF of 22900 and 22914?

We will first find the prime factorization of 22900 and 22914. After we will calculate the factors of 22900 and 22914 and find the biggest common factor number .

Step-1: Prime Factorization of 22900

Prime factors of 22900 are 2, 5, 229. Prime factorization of 22900 in exponential form is:

22900 = 2² × 5² × 229¹

Step-2: Prime Factorization of 22914

Prime factors of 22914 are 2, 3, 19, 67. Prime factorization of 22914 in exponential form is:

22914 = 2¹ × 3² × 19¹ × 67¹

Step-3: Factors of 22900

List of positive integer factors of 22900 that divides 22900 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 229, 458, 916, 1145, 2290, 4580, 5725, 11450

Step-4: Factors of 22914

List of positive integer factors of 22914 that divides 22900 without a remainder.

1, 2, 3, 6, 9, 18, 19, 38, 57, 67, 114, 134, 171, 201, 342, 402, 603, 1206, 1273, 2546, 3819, 7638, 11457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22900 and 22914. The biggest common factor number is the GCF number.
So the greatest common factor 22900 and 22914 is 2.

Also check out the Least Common Multiple of 22900 and 22914