What is the Greatest Common Factor of 96960 and 96975?

Greatest common factor (GCF) of 96960 and 96975 is 15.

GCF(96960,96975) = 15

We will now calculate the prime factors of 96960 and 96975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 96960 and 96975.

How to find the GCF of 96960 and 96975?

We will first find the prime factorization of 96960 and 96975. After we will calculate the factors of 96960 and 96975 and find the biggest common factor number .

Step-1: Prime Factorization of 96960

Prime factors of 96960 are 2, 3, 5, 101. Prime factorization of 96960 in exponential form is:

96960 = 2⁶ × 3¹ × 5¹ × 101¹

Step-2: Prime Factorization of 96975

Prime factors of 96975 are 3, 5, 431. Prime factorization of 96975 in exponential form is:

96975 = 3² × 5² × 431¹

Step-3: Factors of 96960

List of positive integer factors of 96960 that divides 96960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 101, 120, 160, 192, 202, 240, 303, 320, 404, 480, 505, 606, 808, 960, 1010, 1212, 1515, 1616, 2020, 2424, 3030, 3232, 4040, 4848, 6060, 6464, 8080, 9696, 12120, 16160, 19392, 24240, 32320, 48480

Step-4: Factors of 96975

List of positive integer factors of 96975 that divides 96960 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 225, 431, 1293, 2155, 3879, 6465, 10775, 19395, 32325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 96960 and 96975. The biggest common factor number is the GCF number.
So the greatest common factor 96960 and 96975 is 15.

Also check out the Least Common Multiple of 96960 and 96975