What is the Greatest Common Factor of 7509 and 7514?

Greatest common factor (GCF) of 7509 and 7514 is 1.

GCF(7509,7514) = 1

We will now calculate the prime factors of 7509 and 7514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7509 and 7514.

How to find the GCF of 7509 and 7514?

We will first find the prime factorization of 7509 and 7514. After we will calculate the factors of 7509 and 7514 and find the biggest common factor number .

Step-1: Prime Factorization of 7509

Prime factors of 7509 are 3, 2503. Prime factorization of 7509 in exponential form is:

7509 = 3¹ × 2503¹

Step-2: 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-3: Factors of 7509

List of positive integer factors of 7509 that divides 7509 without a remainder.

1, 3, 2503

Step-4: Factors of 7514

List of positive integer factors of 7514 that divides 7509 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7509 and 7514. The biggest common factor number is the GCF number.
So the greatest common factor 7509 and 7514 is 1.

Also check out the Least Common Multiple of 7509 and 7514