What is the Greatest Common Factor of 7524 and 7538?

Greatest common factor (GCF) of 7524 and 7538 is 2.

GCF(7524,7538) = 2

We will now calculate the prime factors of 7524 and 7538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7524 and 7538.

How to find the GCF of 7524 and 7538?

We will first find the prime factorization of 7524 and 7538. After we will calculate the factors of 7524 and 7538 and find the biggest common factor number .

Step-1: Prime Factorization of 7524

Prime factors of 7524 are 2, 3, 11, 19. Prime factorization of 7524 in exponential form is:

7524 = 2² × 3² × 11¹ × 19¹

Step-2: Prime Factorization of 7538

Prime factors of 7538 are 2, 3769. Prime factorization of 7538 in exponential form is:

7538 = 2¹ × 3769¹

Step-3: Factors of 7524

List of positive integer factors of 7524 that divides 7524 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 19, 22, 33, 36, 38, 44, 57, 66, 76, 99, 114, 132, 171, 198, 209, 228, 342, 396, 418, 627, 684, 836, 1254, 1881, 2508, 3762

Step-4: Factors of 7538

List of positive integer factors of 7538 that divides 7524 without a remainder.

1, 2, 3769

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7524 and 7538. The biggest common factor number is the GCF number.
So the greatest common factor 7524 and 7538 is 2.

Also check out the Least Common Multiple of 7524 and 7538