What is the Greatest Common Factor of 30564 and 30576?

Greatest common factor (GCF) of 30564 and 30576 is 12.

GCF(30564,30576) = 12

We will now calculate the prime factors of 30564 and 30576, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30564 and 30576.

How to find the GCF of 30564 and 30576?

We will first find the prime factorization of 30564 and 30576. After we will calculate the factors of 30564 and 30576 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 30576

Prime factors of 30576 are 2, 3, 7, 13. Prime factorization of 30576 in exponential form is:

30576 = 2⁴ × 3¹ × 7² × 13¹

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 30576

List of positive integer factors of 30576 that divides 30564 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 39, 42, 48, 49, 52, 56, 78, 84, 91, 98, 104, 112, 147, 156, 168, 182, 196, 208, 273, 294, 312, 336, 364, 392, 546, 588, 624, 637, 728, 784, 1092, 1176, 1274, 1456, 1911, 2184, 2352, 2548, 3822, 4368, 5096, 7644, 10192, 15288

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30564 and 30576. The biggest common factor number is the GCF number.
So the greatest common factor 30564 and 30576 is 12.

Also check out the Least Common Multiple of 30564 and 30576