What is the Greatest Common Factor of 60960 and 60975?

Greatest common factor (GCF) of 60960 and 60975 is 15.

GCF(60960,60975) = 15

We will now calculate the prime factors of 60960 and 60975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 60960 and 60975.

How to find the GCF of 60960 and 60975?

We will first find the prime factorization of 60960 and 60975. After we will calculate the factors of 60960 and 60975 and find the biggest common factor number .

Step-1: Prime Factorization of 60960

Prime factors of 60960 are 2, 3, 5, 127. Prime factorization of 60960 in exponential form is:

60960 = 2⁵ × 3¹ × 5¹ × 127¹

Step-2: Prime Factorization of 60975

Prime factors of 60975 are 3, 5, 271. Prime factorization of 60975 in exponential form is:

60975 = 3² × 5² × 271¹

Step-3: Factors of 60960

List of positive integer factors of 60960 that divides 60960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 127, 160, 240, 254, 381, 480, 508, 635, 762, 1016, 1270, 1524, 1905, 2032, 2540, 3048, 3810, 4064, 5080, 6096, 7620, 10160, 12192, 15240, 20320, 30480

Step-4: Factors of 60975

List of positive integer factors of 60975 that divides 60960 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 225, 271, 813, 1355, 2439, 4065, 6775, 12195, 20325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 60960 and 60975. The biggest common factor number is the GCF number.
So the greatest common factor 60960 and 60975 is 15.

Also check out the Least Common Multiple of 60960 and 60975