What is the Greatest Common Factor of 30900 and 30912?

Greatest common factor (GCF) of 30900 and 30912 is 12.

GCF(30900,30912) = 12

We will now calculate the prime factors of 30900 and 30912, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30900 and 30912.

How to find the GCF of 30900 and 30912?

We will first find the prime factorization of 30900 and 30912. After we will calculate the factors of 30900 and 30912 and find the biggest common factor number .

Step-1: Prime Factorization of 30900

Prime factors of 30900 are 2, 3, 5, 103. Prime factorization of 30900 in exponential form is:

30900 = 2² × 3¹ × 5² × 103¹

Step-2: Prime Factorization of 30912

Prime factors of 30912 are 2, 3, 7, 23. Prime factorization of 30912 in exponential form is:

30912 = 2⁶ × 3¹ × 7¹ × 23¹

Step-3: Factors of 30900

List of positive integer factors of 30900 that divides 30900 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 103, 150, 206, 300, 309, 412, 515, 618, 1030, 1236, 1545, 2060, 2575, 3090, 5150, 6180, 7725, 10300, 15450

Step-4: Factors of 30912

List of positive integer factors of 30912 that divides 30900 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 32, 42, 46, 48, 56, 64, 69, 84, 92, 96, 112, 138, 161, 168, 184, 192, 224, 276, 322, 336, 368, 448, 483, 552, 644, 672, 736, 966, 1104, 1288, 1344, 1472, 1932, 2208, 2576, 3864, 4416, 5152, 7728, 10304, 15456

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30900 and 30912. The biggest common factor number is the GCF number.
So the greatest common factor 30900 and 30912 is 12.

Also check out the Least Common Multiple of 30900 and 30912