What is the Greatest Common Factor of 7527 and 7540?

Greatest common factor (GCF) of 7527 and 7540 is 13.

GCF(7527,7540) = 13

We will now calculate the prime factors of 7527 and 7540, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7527 and 7540.

How to find the GCF of 7527 and 7540?

We will first find the prime factorization of 7527 and 7540. After we will calculate the factors of 7527 and 7540 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 7540

Prime factors of 7540 are 2, 5, 13, 29. Prime factorization of 7540 in exponential form is:

7540 = 2² × 5¹ × 13¹ × 29¹

Step-3: Factors of 7527

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

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

Step-4: Factors of 7540

List of positive integer factors of 7540 that divides 7527 without a remainder.

1, 2, 4, 5, 10, 13, 20, 26, 29, 52, 58, 65, 116, 130, 145, 260, 290, 377, 580, 754, 1508, 1885, 3770

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7527 and 7540. The biggest common factor number is the GCF number.
So the greatest common factor 7527 and 7540 is 13.

Also check out the Least Common Multiple of 7527 and 7540