What is the Greatest Common Factor of 14404 and 14417?

Greatest common factor (GCF) of 14404 and 14417 is 13.

GCF(14404,14417) = 13

We will now calculate the prime factors of 14404 and 14417, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14404 and 14417.

How to find the GCF of 14404 and 14417?

We will first find the prime factorization of 14404 and 14417. After we will calculate the factors of 14404 and 14417 and find the biggest common factor number .

Step-1: Prime Factorization of 14404

Prime factors of 14404 are 2, 13, 277. Prime factorization of 14404 in exponential form is:

14404 = 2² × 13¹ × 277¹

Step-2: Prime Factorization of 14417

Prime factors of 14417 are 13, 1109. Prime factorization of 14417 in exponential form is:

14417 = 13¹ × 1109¹

Step-3: Factors of 14404

List of positive integer factors of 14404 that divides 14404 without a remainder.

1, 2, 4, 13, 26, 52, 277, 554, 1108, 3601, 7202

Step-4: Factors of 14417

List of positive integer factors of 14417 that divides 14404 without a remainder.

1, 13, 1109

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14404 and 14417. The biggest common factor number is the GCF number.
So the greatest common factor 14404 and 14417 is 13.

Also check out the Least Common Multiple of 14404 and 14417