What is the Greatest Common Factor of 7514 and 7527?

Greatest common factor (GCF) of 7514 and 7527 is 13.

GCF(7514,7527) = 13

We will now calculate the prime factors of 7514 and 7527, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7514 and 7527.

How to find the GCF of 7514 and 7527?

We will first find the prime factorization of 7514 and 7527. After we will calculate the factors of 7514 and 7527 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 7527

Prime factors of 7527 are 3, 13, 193. Prime factorization of 7527 in exponential form is:

7527 = 3¹ × 13¹ × 193¹

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 7527

List of positive integer factors of 7527 that divides 7514 without a remainder.

1, 3, 13, 39, 193, 579, 2509

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7514 and 7527. The biggest common factor number is the GCF number.
So the greatest common factor 7514 and 7527 is 13.

Also check out the Least Common Multiple of 7514 and 7527