What is the Greatest Common Factor of 2249 and 2262?

Greatest common factor (GCF) of 2249 and 2262 is 13.

GCF(2249,2262) = 13

We will now calculate the prime factors of 2249 and 2262, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2249 and 2262.

How to find the GCF of 2249 and 2262?

We will first find the prime factorization of 2249 and 2262. After we will calculate the factors of 2249 and 2262 and find the biggest common factor number .

Step-1: Prime Factorization of 2249

Prime factors of 2249 are 13, 173. Prime factorization of 2249 in exponential form is:

2249 = 13¹ × 173¹

Step-2: Prime Factorization of 2262

Prime factors of 2262 are 2, 3, 13, 29. Prime factorization of 2262 in exponential form is:

2262 = 2¹ × 3¹ × 13¹ × 29¹

Step-3: Factors of 2249

List of positive integer factors of 2249 that divides 2249 without a remainder.

1, 13, 173

Step-4: Factors of 2262

List of positive integer factors of 2262 that divides 2249 without a remainder.

1, 2, 3, 6, 13, 26, 29, 39, 58, 78, 87, 174, 377, 754, 1131

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2249 and 2262. The biggest common factor number is the GCF number.
So the greatest common factor 2249 and 2262 is 13.

Also check out the Least Common Multiple of 2249 and 2262