What is the Greatest Common Factor of 15960 and 15975?

Greatest common factor (GCF) of 15960 and 15975 is 15.

GCF(15960,15975) = 15

We will now calculate the prime factors of 15960 and 15975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15960 and 15975.

How to find the GCF of 15960 and 15975?

We will first find the prime factorization of 15960 and 15975. After we will calculate the factors of 15960 and 15975 and find the biggest common factor number .

Step-1: Prime Factorization of 15960

Prime factors of 15960 are 2, 3, 5, 7, 19. Prime factorization of 15960 in exponential form is:

15960 = 2³ × 3¹ × 5¹ × 7¹ × 19¹

Step-2: Prime Factorization of 15975

Prime factors of 15975 are 3, 5, 71. Prime factorization of 15975 in exponential form is:

15975 = 3² × 5² × 71¹

Step-3: Factors of 15960

List of positive integer factors of 15960 that divides 15960 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 19, 20, 21, 24, 28, 30, 35, 38, 40, 42, 56, 57, 60, 70, 76, 84, 95, 105, 114, 120, 133, 140, 152, 168, 190, 210, 228, 266, 280, 285, 380, 399, 420, 456, 532, 570, 665, 760, 798, 840, 1064, 1140, 1330, 1596, 1995, 2280, 2660, 3192, 3990, 5320, 7980

Step-4: Factors of 15975

List of positive integer factors of 15975 that divides 15960 without a remainder.

1, 3, 5, 9, 15, 25, 45, 71, 75, 213, 225, 355, 639, 1065, 1775, 3195, 5325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15960 and 15975. The biggest common factor number is the GCF number.
So the greatest common factor 15960 and 15975 is 15.

Also check out the Least Common Multiple of 15960 and 15975