What is the Greatest Common Factor of 30909 and 30924?

Greatest common factor (GCF) of 30909 and 30924 is 3.

GCF(30909,30924) = 3

We will now calculate the prime factors of 30909 and 30924, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30909 and 30924.

How to find the GCF of 30909 and 30924?

We will first find the prime factorization of 30909 and 30924. After we will calculate the factors of 30909 and 30924 and find the biggest common factor number .

Step-1: Prime Factorization of 30909

Prime factors of 30909 are 3, 10303. Prime factorization of 30909 in exponential form is:

30909 = 3¹ × 10303¹

Step-2: Prime Factorization of 30924

Prime factors of 30924 are 2, 3, 859. Prime factorization of 30924 in exponential form is:

30924 = 2² × 3² × 859¹

Step-3: Factors of 30909

List of positive integer factors of 30909 that divides 30909 without a remainder.

1, 3, 10303

Step-4: Factors of 30924

List of positive integer factors of 30924 that divides 30909 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 859, 1718, 2577, 3436, 5154, 7731, 10308, 15462

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30909 and 30924. The biggest common factor number is the GCF number.
So the greatest common factor 30909 and 30924 is 3.

Also check out the Least Common Multiple of 30909 and 30924