What is the Greatest Common Factor of 7254 and 7260?

Greatest common factor (GCF) of 7254 and 7260 is 6.

GCF(7254,7260) = 6

We will now calculate the prime factors of 7254 and 7260, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7254 and 7260.

How to find the GCF of 7254 and 7260?

We will first find the prime factorization of 7254 and 7260. After we will calculate the factors of 7254 and 7260 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 7260

Prime factors of 7260 are 2, 3, 5, 11. Prime factorization of 7260 in exponential form is:

7260 = 2² × 3¹ × 5¹ × 11²

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 7260

List of positive integer factors of 7260 that divides 7254 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 121, 132, 165, 220, 242, 330, 363, 484, 605, 660, 726, 1210, 1452, 1815, 2420, 3630

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7254 and 7260. The biggest common factor number is the GCF number.
So the greatest common factor 7254 and 7260 is 6.

Also check out the Least Common Multiple of 7254 and 7260