What is the Greatest Common Factor of 12960 and 12975?

Greatest common factor (GCF) of 12960 and 12975 is 15.

GCF(12960,12975) = 15

We will now calculate the prime factors of 12960 and 12975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12960 and 12975.

How to find the GCF of 12960 and 12975?

We will first find the prime factorization of 12960 and 12975. After we will calculate the factors of 12960 and 12975 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 12975

Prime factors of 12975 are 3, 5, 173. Prime factorization of 12975 in exponential form is:

12975 = 3¹ × 5² × 173¹

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 12975

List of positive integer factors of 12975 that divides 12960 without a remainder.

1, 3, 5, 15, 25, 75, 173, 519, 865, 2595, 4325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12960 and 12975. The biggest common factor number is the GCF number.
So the greatest common factor 12960 and 12975 is 15.

Also check out the Least Common Multiple of 12960 and 12975