What is the Greatest Common Factor of 14623 and 14637?

Greatest common factor (GCF) of 14623 and 14637 is 7.

GCF(14623,14637) = 7

We will now calculate the prime factors of 14623 and 14637, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14623 and 14637.

How to find the GCF of 14623 and 14637?

We will first find the prime factorization of 14623 and 14637. After we will calculate the factors of 14623 and 14637 and find the biggest common factor number .

Step-1: Prime Factorization of 14623

Prime factors of 14623 are 7, 2089. Prime factorization of 14623 in exponential form is:

14623 = 7¹ × 2089¹

Step-2: Prime Factorization of 14637

Prime factors of 14637 are 3, 7, 17, 41. Prime factorization of 14637 in exponential form is:

14637 = 3¹ × 7¹ × 17¹ × 41¹

Step-3: Factors of 14623

List of positive integer factors of 14623 that divides 14623 without a remainder.

1, 7, 2089

Step-4: Factors of 14637

List of positive integer factors of 14637 that divides 14623 without a remainder.

1, 3, 7, 17, 21, 41, 51, 119, 123, 287, 357, 697, 861, 2091, 4879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14623 and 14637. The biggest common factor number is the GCF number.
So the greatest common factor 14623 and 14637 is 7.

Also check out the Least Common Multiple of 14623 and 14637