What is the Greatest Common Factor of 3960 and 3975?

Greatest common factor (GCF) of 3960 and 3975 is 15.

GCF(3960,3975) = 15

We will now calculate the prime factors of 3960 and 3975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3960 and 3975.

How to find the GCF of 3960 and 3975?

We will first find the prime factorization of 3960 and 3975. After we will calculate the factors of 3960 and 3975 and find the biggest common factor number .

Step-1: Prime Factorization of 3960

Prime factors of 3960 are 2, 3, 5, 11. Prime factorization of 3960 in exponential form is:

3960 = 2³ × 3² × 5¹ × 11¹

Step-2: Prime Factorization of 3975

Prime factors of 3975 are 3, 5, 53. Prime factorization of 3975 in exponential form is:

3975 = 3¹ × 5² × 53¹

Step-3: Factors of 3960

List of positive integer factors of 3960 that divides 3960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 55, 60, 66, 72, 88, 90, 99, 110, 120, 132, 165, 180, 198, 220, 264, 330, 360, 396, 440, 495, 660, 792, 990, 1320, 1980

Step-4: Factors of 3975

List of positive integer factors of 3975 that divides 3960 without a remainder.

1, 3, 5, 15, 25, 53, 75, 159, 265, 795, 1325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3960 and 3975. The biggest common factor number is the GCF number.
So the greatest common factor 3960 and 3975 is 15.

Also check out the Least Common Multiple of 3960 and 3975