What is the Greatest Common Factor of 30960 and 30975?

Greatest common factor (GCF) of 30960 and 30975 is 15.

GCF(30960,30975) = 15

We will now calculate the prime factors of 30960 and 30975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30960 and 30975.

How to find the GCF of 30960 and 30975?

We will first find the prime factorization of 30960 and 30975. After we will calculate the factors of 30960 and 30975 and find the biggest common factor number .

Step-1: Prime Factorization of 30960

Prime factors of 30960 are 2, 3, 5, 43. Prime factorization of 30960 in exponential form is:

30960 = 2⁴ × 3² × 5¹ × 43¹

Step-2: Prime Factorization of 30975

Prime factors of 30975 are 3, 5, 7, 59. Prime factorization of 30975 in exponential form is:

30975 = 3¹ × 5² × 7¹ × 59¹

Step-3: Factors of 30960

List of positive integer factors of 30960 that divides 30960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 43, 45, 48, 60, 72, 80, 86, 90, 120, 129, 144, 172, 180, 215, 240, 258, 344, 360, 387, 430, 516, 645, 688, 720, 774, 860, 1032, 1290, 1548, 1720, 1935, 2064, 2580, 3096, 3440, 3870, 5160, 6192, 7740, 10320, 15480

Step-4: Factors of 30975

List of positive integer factors of 30975 that divides 30960 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 59, 75, 105, 175, 177, 295, 413, 525, 885, 1239, 1475, 2065, 4425, 6195, 10325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30960 and 30975. The biggest common factor number is the GCF number.
So the greatest common factor 30960 and 30975 is 15.

Also check out the Least Common Multiple of 30960 and 30975