What is the Greatest Common Factor of 12648 and 12665?

Greatest common factor (GCF) of 12648 and 12665 is 17.

GCF(12648,12665) = 17

We will now calculate the prime factors of 12648 and 12665, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12648 and 12665.

How to find the GCF of 12648 and 12665?

We will first find the prime factorization of 12648 and 12665. After we will calculate the factors of 12648 and 12665 and find the biggest common factor number .

Step-1: Prime Factorization of 12648

Prime factors of 12648 are 2, 3, 17, 31. Prime factorization of 12648 in exponential form is:

12648 = 2³ × 3¹ × 17¹ × 31¹

Step-2: Prime Factorization of 12665

Prime factors of 12665 are 5, 17, 149. Prime factorization of 12665 in exponential form is:

12665 = 5¹ × 17¹ × 149¹

Step-3: Factors of 12648

List of positive integer factors of 12648 that divides 12648 without a remainder.

1, 2, 3, 4, 6, 8, 12, 17, 24, 31, 34, 51, 62, 68, 93, 102, 124, 136, 186, 204, 248, 372, 408, 527, 744, 1054, 1581, 2108, 3162, 4216, 6324

Step-4: Factors of 12665

List of positive integer factors of 12665 that divides 12648 without a remainder.

1, 5, 17, 85, 149, 745, 2533

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12648 and 12665. The biggest common factor number is the GCF number.
So the greatest common factor 12648 and 12665 is 17.

Also check out the Least Common Multiple of 12648 and 12665