What is the Greatest Common Factor of 7254 and 7262?

Greatest common factor (GCF) of 7254 and 7262 is 2.

GCF(7254,7262) = 2

We will now calculate the prime factors of 7254 and 7262, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7254 and 7262.

How to find the GCF of 7254 and 7262?

We will first find the prime factorization of 7254 and 7262. After we will calculate the factors of 7254 and 7262 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 7262

Prime factors of 7262 are 2, 3631. Prime factorization of 7262 in exponential form is:

7262 = 2¹ × 3631¹

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 7262

List of positive integer factors of 7262 that divides 7254 without a remainder.

1, 2, 3631

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7254 and 7262. The biggest common factor number is the GCF number.
So the greatest common factor 7254 and 7262 is 2.

Also check out the Least Common Multiple of 7254 and 7262