What is the Greatest Common Factor of 14606 and 14625?

Greatest common factor (GCF) of 14606 and 14625 is 1.

GCF(14606,14625) = 1

We will now calculate the prime factors of 14606 and 14625, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14606 and 14625.

How to find the GCF of 14606 and 14625?

We will first find the prime factorization of 14606 and 14625. After we will calculate the factors of 14606 and 14625 and find the biggest common factor number .

Step-1: Prime Factorization of 14606

Prime factors of 14606 are 2, 67, 109. Prime factorization of 14606 in exponential form is:

14606 = 2¹ × 67¹ × 109¹

Step-2: Prime Factorization of 14625

Prime factors of 14625 are 3, 5, 13. Prime factorization of 14625 in exponential form is:

14625 = 3² × 5³ × 13¹

Step-3: Factors of 14606

List of positive integer factors of 14606 that divides 14606 without a remainder.

1, 2, 67, 109, 134, 218, 7303

Step-4: Factors of 14625

List of positive integer factors of 14625 that divides 14606 without a remainder.

1, 3, 5, 9, 13, 15, 25, 39, 45, 65, 75, 117, 125, 195, 225, 325, 375, 585, 975, 1125, 1625, 2925, 4875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14606 and 14625. The biggest common factor number is the GCF number.
So the greatest common factor 14606 and 14625 is 1.

Also check out the Least Common Multiple of 14606 and 14625