What is the Greatest Common Factor of 7254 and 7267?

Greatest common factor (GCF) of 7254 and 7267 is 13.

GCF(7254,7267) = 13

We will now calculate the prime factors of 7254 and 7267, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7254 and 7267.

How to find the GCF of 7254 and 7267?

We will first find the prime factorization of 7254 and 7267. After we will calculate the factors of 7254 and 7267 and find the biggest common factor number .

Step-1: Prime Factorization of 7254

Prime factors of 7254 are 2, 3, 13, 31. Prime factorization of 7254 in exponential form is:

7254 = 2¹ × 3² × 13¹ × 31¹

Step-2: Prime Factorization of 7267

Prime factors of 7267 are 13, 43. Prime factorization of 7267 in exponential form is:

7267 = 13² × 43¹

Step-3: Factors of 7254

List of positive integer factors of 7254 that divides 7254 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 31, 39, 62, 78, 93, 117, 186, 234, 279, 403, 558, 806, 1209, 2418, 3627

Step-4: Factors of 7267

List of positive integer factors of 7267 that divides 7254 without a remainder.

1, 13, 43, 169, 559

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7254 and 7267. The biggest common factor number is the GCF number.
So the greatest common factor 7254 and 7267 is 13.

Also check out the Least Common Multiple of 7254 and 7267