What is the Greatest Common Factor of 14892 and 14909?

Greatest common factor (GCF) of 14892 and 14909 is 17.

GCF(14892,14909) = 17

We will now calculate the prime factors of 14892 and 14909, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14892 and 14909.

How to find the GCF of 14892 and 14909?

We will first find the prime factorization of 14892 and 14909. After we will calculate the factors of 14892 and 14909 and find the biggest common factor number .

Step-1: Prime Factorization of 14892

Prime factors of 14892 are 2, 3, 17, 73. Prime factorization of 14892 in exponential form is:

14892 = 2² × 3¹ × 17¹ × 73¹

Step-2: Prime Factorization of 14909

Prime factors of 14909 are 17, 877. Prime factorization of 14909 in exponential form is:

14909 = 17¹ × 877¹

Step-3: Factors of 14892

List of positive integer factors of 14892 that divides 14892 without a remainder.

1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 73, 102, 146, 204, 219, 292, 438, 876, 1241, 2482, 3723, 4964, 7446

Step-4: Factors of 14909

List of positive integer factors of 14909 that divides 14892 without a remainder.

1, 17, 877

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14892 and 14909. The biggest common factor number is the GCF number.
So the greatest common factor 14892 and 14909 is 17.

Also check out the Least Common Multiple of 14892 and 14909