What is the Greatest Common Factor of 30912 and 30930?

Greatest common factor (GCF) of 30912 and 30930 is 6.

GCF(30912,30930) = 6

We will now calculate the prime factors of 30912 and 30930, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30912 and 30930.

How to find the GCF of 30912 and 30930?

We will first find the prime factorization of 30912 and 30930. After we will calculate the factors of 30912 and 30930 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 30930

Prime factors of 30930 are 2, 3, 5, 1031. Prime factorization of 30930 in exponential form is:

30930 = 2¹ × 3¹ × 5¹ × 1031¹

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 30930

List of positive integer factors of 30930 that divides 30912 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 1031, 2062, 3093, 5155, 6186, 10310, 15465

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30912 and 30930. The biggest common factor number is the GCF number.
So the greatest common factor 30912 and 30930 is 6.

Also check out the Least Common Multiple of 30912 and 30930