What is the Greatest Common Factor of 30675 and 30684?

Greatest common factor (GCF) of 30675 and 30684 is 3.

GCF(30675,30684) = 3

We will now calculate the prime factors of 30675 and 30684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30675 and 30684.

How to find the GCF of 30675 and 30684?

We will first find the prime factorization of 30675 and 30684. After we will calculate the factors of 30675 and 30684 and find the biggest common factor number .

Step-1: Prime Factorization of 30675

Prime factors of 30675 are 3, 5, 409. Prime factorization of 30675 in exponential form is:

30675 = 3¹ × 5² × 409¹

Step-2: Prime Factorization of 30684

Prime factors of 30684 are 2, 3, 2557. Prime factorization of 30684 in exponential form is:

30684 = 2² × 3¹ × 2557¹

Step-3: Factors of 30675

List of positive integer factors of 30675 that divides 30675 without a remainder.

1, 3, 5, 15, 25, 75, 409, 1227, 2045, 6135, 10225

Step-4: Factors of 30684

List of positive integer factors of 30684 that divides 30675 without a remainder.

1, 2, 3, 4, 6, 12, 2557, 5114, 7671, 10228, 15342

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30675 and 30684. The biggest common factor number is the GCF number.
So the greatest common factor 30675 and 30684 is 3.

Also check out the Least Common Multiple of 30675 and 30684