What is the Greatest Common Factor of 30975 and 30980?

Greatest common factor (GCF) of 30975 and 30980 is 5.

GCF(30975,30980) = 5

We will now calculate the prime factors of 30975 and 30980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30975 and 30980.

How to find the GCF of 30975 and 30980?

We will first find the prime factorization of 30975 and 30980. After we will calculate the factors of 30975 and 30980 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 30980

Prime factors of 30980 are 2, 5, 1549. Prime factorization of 30980 in exponential form is:

30980 = 2² × 5¹ × 1549¹

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 30980

List of positive integer factors of 30980 that divides 30975 without a remainder.

1, 2, 4, 5, 10, 20, 1549, 3098, 6196, 7745, 15490

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30975 and 30980. The biggest common factor number is the GCF number.
So the greatest common factor 30975 and 30980 is 5.

Also check out the Least Common Multiple of 30975 and 30980