What is the Greatest Common Factor of 30975 and 30990?

Greatest common factor (GCF) of 30975 and 30990 is 15.

GCF(30975,30990) = 15

We will now calculate the prime factors of 30975 and 30990, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30975 and 30990.

How to find the GCF of 30975 and 30990?

We will first find the prime factorization of 30975 and 30990. After we will calculate the factors of 30975 and 30990 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30990

Prime factors of 30990 are 2, 3, 5, 1033. Prime factorization of 30990 in exponential form is:

30990 = 2¹ × 3¹ × 5¹ × 1033¹

Step-3: Factors of 30975

List of positive integer factors of 30975 that divides 30975 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

Step-4: Factors of 30990

List of positive integer factors of 30990 that divides 30975 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 1033, 2066, 3099, 5165, 6198, 10330, 15495

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30975 and 30990. The biggest common factor number is the GCF number.
So the greatest common factor 30975 and 30990 is 15.

Also check out the Least Common Multiple of 30975 and 30990