What is the Greatest Common Factor of 30816 and 30832?

Greatest common factor (GCF) of 30816 and 30832 is 16.

GCF(30816,30832) = 16

We will now calculate the prime factors of 30816 and 30832, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30816 and 30832.

How to find the GCF of 30816 and 30832?

We will first find the prime factorization of 30816 and 30832. After we will calculate the factors of 30816 and 30832 and find the biggest common factor number .

Step-1: Prime Factorization of 30816

Prime factors of 30816 are 2, 3, 107. Prime factorization of 30816 in exponential form is:

30816 = 2⁵ × 3² × 107¹

Step-2: Prime Factorization of 30832

Prime factors of 30832 are 2, 41, 47. Prime factorization of 30832 in exponential form is:

30832 = 2⁴ × 41¹ × 47¹

Step-3: Factors of 30816

List of positive integer factors of 30816 that divides 30816 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 107, 144, 214, 288, 321, 428, 642, 856, 963, 1284, 1712, 1926, 2568, 3424, 3852, 5136, 7704, 10272, 15408

Step-4: Factors of 30832

List of positive integer factors of 30832 that divides 30816 without a remainder.

1, 2, 4, 8, 16, 41, 47, 82, 94, 164, 188, 328, 376, 656, 752, 1927, 3854, 7708, 15416

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30816 and 30832. The biggest common factor number is the GCF number.
So the greatest common factor 30816 and 30832 is 16.

Also check out the Least Common Multiple of 30816 and 30832