What is the Greatest Common Factor of 17524 and 17538?

Greatest common factor (GCF) of 17524 and 17538 is 2.

GCF(17524,17538) = 2

We will now calculate the prime factors of 17524 and 17538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17524 and 17538.

How to find the GCF of 17524 and 17538?

We will first find the prime factorization of 17524 and 17538. After we will calculate the factors of 17524 and 17538 and find the biggest common factor number .

Step-1: Prime Factorization of 17524

Prime factors of 17524 are 2, 13, 337. Prime factorization of 17524 in exponential form is:

17524 = 2² × 13¹ × 337¹

Step-2: Prime Factorization of 17538

Prime factors of 17538 are 2, 3, 37, 79. Prime factorization of 17538 in exponential form is:

17538 = 2¹ × 3¹ × 37¹ × 79¹

Step-3: Factors of 17524

List of positive integer factors of 17524 that divides 17524 without a remainder.

1, 2, 4, 13, 26, 52, 337, 674, 1348, 4381, 8762

Step-4: Factors of 17538

List of positive integer factors of 17538 that divides 17524 without a remainder.

1, 2, 3, 6, 37, 74, 79, 111, 158, 222, 237, 474, 2923, 5846, 8769

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17524 and 17538. The biggest common factor number is the GCF number.
So the greatest common factor 17524 and 17538 is 2.

Also check out the Least Common Multiple of 17524 and 17538