What is the Greatest Common Factor of 30384 and 30396?

Greatest common factor (GCF) of 30384 and 30396 is 12.

GCF(30384,30396) = 12

We will now calculate the prime factors of 30384 and 30396, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30384 and 30396.

How to find the GCF of 30384 and 30396?

We will first find the prime factorization of 30384 and 30396. After we will calculate the factors of 30384 and 30396 and find the biggest common factor number .

Step-1: Prime Factorization of 30384

Prime factors of 30384 are 2, 3, 211. Prime factorization of 30384 in exponential form is:

30384 = 2⁴ × 3² × 211¹

Step-2: Prime Factorization of 30396

Prime factors of 30396 are 2, 3, 17, 149. Prime factorization of 30396 in exponential form is:

30396 = 2² × 3¹ × 17¹ × 149¹

Step-3: Factors of 30384

List of positive integer factors of 30384 that divides 30384 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 211, 422, 633, 844, 1266, 1688, 1899, 2532, 3376, 3798, 5064, 7596, 10128, 15192

Step-4: Factors of 30396

List of positive integer factors of 30396 that divides 30384 without a remainder.

1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 149, 204, 298, 447, 596, 894, 1788, 2533, 5066, 7599, 10132, 15198

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30384 and 30396. The biggest common factor number is the GCF number.
So the greatest common factor 30384 and 30396 is 12.

Also check out the Least Common Multiple of 30384 and 30396