What is the Greatest Common Factor of 30564 and 30582?

Greatest common factor (GCF) of 30564 and 30582 is 18.

GCF(30564,30582) = 18

We will now calculate the prime factors of 30564 and 30582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30564 and 30582.

How to find the GCF of 30564 and 30582?

We will first find the prime factorization of 30564 and 30582. After we will calculate the factors of 30564 and 30582 and find the biggest common factor number .

Step-1: Prime Factorization of 30564

Prime factors of 30564 are 2, 3, 283. Prime factorization of 30564 in exponential form is:

30564 = 2² × 3³ × 283¹

Step-2: Prime Factorization of 30582

Prime factors of 30582 are 2, 3, 1699. Prime factorization of 30582 in exponential form is:

30582 = 2¹ × 3² × 1699¹

Step-3: Factors of 30564

List of positive integer factors of 30564 that divides 30564 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 283, 566, 849, 1132, 1698, 2547, 3396, 5094, 7641, 10188, 15282

Step-4: Factors of 30582

List of positive integer factors of 30582 that divides 30564 without a remainder.

1, 2, 3, 6, 9, 18, 1699, 3398, 5097, 10194, 15291

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30564 and 30582. The biggest common factor number is the GCF number.
So the greatest common factor 30564 and 30582 is 18.

Also check out the Least Common Multiple of 30564 and 30582