What is the Greatest Common Factor of 30912 and 30928?

Greatest common factor (GCF) of 30912 and 30928 is 16.

GCF(30912,30928) = 16

We will now calculate the prime factors of 30912 and 30928, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30912 and 30928.

How to find the GCF of 30912 and 30928?

We will first find the prime factorization of 30912 and 30928. After we will calculate the factors of 30912 and 30928 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30928

Prime factors of 30928 are 2, 1933. Prime factorization of 30928 in exponential form is:

30928 = 2⁴ × 1933¹

Step-3: Factors of 30912

List of positive integer factors of 30912 that divides 30912 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

Step-4: Factors of 30928

List of positive integer factors of 30928 that divides 30912 without a remainder.

1, 2, 4, 8, 16, 1933, 3866, 7732, 15464

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30912 and 30928. The biggest common factor number is the GCF number.
So the greatest common factor 30912 and 30928 is 16.

Also check out the Least Common Multiple of 30912 and 30928