What is the Greatest Common Factor of 2509 and 2522?

Greatest common factor (GCF) of 2509 and 2522 is 13.

GCF(2509,2522) = 13

We will now calculate the prime factors of 2509 and 2522, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2509 and 2522.

How to find the GCF of 2509 and 2522?

We will first find the prime factorization of 2509 and 2522. After we will calculate the factors of 2509 and 2522 and find the biggest common factor number .

Step-1: Prime Factorization of 2509

Prime factors of 2509 are 13, 193. Prime factorization of 2509 in exponential form is:

2509 = 13¹ × 193¹

Step-2: Prime Factorization of 2522

Prime factors of 2522 are 2, 13, 97. Prime factorization of 2522 in exponential form is:

2522 = 2¹ × 13¹ × 97¹

Step-3: Factors of 2509

List of positive integer factors of 2509 that divides 2509 without a remainder.

1, 13, 193

Step-4: Factors of 2522

List of positive integer factors of 2522 that divides 2509 without a remainder.

1, 2, 13, 26, 97, 194, 1261

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2509 and 2522. The biggest common factor number is the GCF number.
So the greatest common factor 2509 and 2522 is 13.

Also check out the Least Common Multiple of 2509 and 2522