What is the Greatest Common Factor of 7514 and 7526?

Greatest common factor (GCF) of 7514 and 7526 is 2.

GCF(7514,7526) = 2

We will now calculate the prime factors of 7514 and 7526, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7514 and 7526.

How to find the GCF of 7514 and 7526?

We will first find the prime factorization of 7514 and 7526. After we will calculate the factors of 7514 and 7526 and find the biggest common factor number .

Step-1: Prime Factorization of 7514

Prime factors of 7514 are 2, 13, 17. Prime factorization of 7514 in exponential form is:

7514 = 2¹ × 13¹ × 17²

Step-2: Prime Factorization of 7526

Prime factors of 7526 are 2, 53, 71. Prime factorization of 7526 in exponential form is:

7526 = 2¹ × 53¹ × 71¹

Step-3: Factors of 7514

List of positive integer factors of 7514 that divides 7514 without a remainder.

1, 2, 13, 17, 26, 34, 221, 289, 442, 578, 3757

Step-4: Factors of 7526

List of positive integer factors of 7526 that divides 7514 without a remainder.

1, 2, 53, 71, 106, 142, 3763

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7514 and 7526. The biggest common factor number is the GCF number.
So the greatest common factor 7514 and 7526 is 2.

Also check out the Least Common Multiple of 7514 and 7526