What is the Greatest Common Factor of 12960 and 12965?

Greatest common factor (GCF) of 12960 and 12965 is 5.

GCF(12960,12965) = 5

We will now calculate the prime factors of 12960 and 12965, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12960 and 12965.

How to find the GCF of 12960 and 12965?

We will first find the prime factorization of 12960 and 12965. After we will calculate the factors of 12960 and 12965 and find the biggest common factor number .

Step-1: Prime Factorization of 12960

Prime factors of 12960 are 2, 3, 5. Prime factorization of 12960 in exponential form is:

12960 = 2⁵ × 3⁴ × 5¹

Step-2: Prime Factorization of 12965

Prime factors of 12965 are 5, 2593. Prime factorization of 12965 in exponential form is:

12965 = 5¹ × 2593¹

Step-3: Factors of 12960

List of positive integer factors of 12960 that divides 12960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 81, 90, 96, 108, 120, 135, 144, 160, 162, 180, 216, 240, 270, 288, 324, 360, 405, 432, 480, 540, 648, 720, 810, 864, 1080, 1296, 1440, 1620, 2160, 2592, 3240, 4320, 6480

Step-4: Factors of 12965

List of positive integer factors of 12965 that divides 12960 without a remainder.

1, 5, 2593

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12960 and 12965. The biggest common factor number is the GCF number.
So the greatest common factor 12960 and 12965 is 5.

Also check out the Least Common Multiple of 12960 and 12965