What is the Greatest Common Factor of 7538 and 7544?

Greatest common factor (GCF) of 7538 and 7544 is 2.

GCF(7538,7544) = 2

We will now calculate the prime factors of 7538 and 7544, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7538 and 7544.

How to find the GCF of 7538 and 7544?

We will first find the prime factorization of 7538 and 7544. After we will calculate the factors of 7538 and 7544 and find the biggest common factor number .

Step-1: Prime Factorization of 7538

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

7538 = 2¹ × 3769¹

Step-2: Prime Factorization of 7544

Prime factors of 7544 are 2, 23, 41. Prime factorization of 7544 in exponential form is:

7544 = 2³ × 23¹ × 41¹

Step-3: Factors of 7538

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

1, 2, 3769

Step-4: Factors of 7544

List of positive integer factors of 7544 that divides 7538 without a remainder.

1, 2, 4, 8, 23, 41, 46, 82, 92, 164, 184, 328, 943, 1886, 3772

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7538 and 7544. The biggest common factor number is the GCF number.
So the greatest common factor 7538 and 7544 is 2.

Also check out the Least Common Multiple of 7538 and 7544