What is the Greatest Common Factor of 7254 and 7272?

Greatest common factor (GCF) of 7254 and 7272 is 18.

GCF(7254,7272) = 18

We will now calculate the prime factors of 7254 and 7272, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7254 and 7272.

How to find the GCF of 7254 and 7272?

We will first find the prime factorization of 7254 and 7272. After we will calculate the factors of 7254 and 7272 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 7272

Prime factors of 7272 are 2, 3, 101. Prime factorization of 7272 in exponential form is:

7272 = 2³ × 3² × 101¹

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 7272

List of positive integer factors of 7272 that divides 7254 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 101, 202, 303, 404, 606, 808, 909, 1212, 1818, 2424, 3636

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7254 and 7272. The biggest common factor number is the GCF number.
So the greatest common factor 7254 and 7272 is 18.

Also check out the Least Common Multiple of 7254 and 7272