What is the Greatest Common Factor of 14523 and 14538?

Greatest common factor (GCF) of 14523 and 14538 is 3.

GCF(14523,14538) = 3

We will now calculate the prime factors of 14523 and 14538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14523 and 14538.

How to find the GCF of 14523 and 14538?

We will first find the prime factorization of 14523 and 14538. After we will calculate the factors of 14523 and 14538 and find the biggest common factor number .

Step-1: Prime Factorization of 14523

Prime factors of 14523 are 3, 47, 103. Prime factorization of 14523 in exponential form is:

14523 = 3¹ × 47¹ × 103¹

Step-2: Prime Factorization of 14538

Prime factors of 14538 are 2, 3, 2423. Prime factorization of 14538 in exponential form is:

14538 = 2¹ × 3¹ × 2423¹

Step-3: Factors of 14523

List of positive integer factors of 14523 that divides 14523 without a remainder.

1, 3, 47, 103, 141, 309, 4841

Step-4: Factors of 14538

List of positive integer factors of 14538 that divides 14523 without a remainder.

1, 2, 3, 6, 2423, 4846, 7269

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14523 and 14538. The biggest common factor number is the GCF number.
So the greatest common factor 14523 and 14538 is 3.

Also check out the Least Common Multiple of 14523 and 14538