What is the Greatest Common Factor of 30800 and 30816?

Greatest common factor (GCF) of 30800 and 30816 is 16.

GCF(30800,30816) = 16

We will now calculate the prime factors of 30800 and 30816, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30800 and 30816.

How to find the GCF of 30800 and 30816?

We will first find the prime factorization of 30800 and 30816. After we will calculate the factors of 30800 and 30816 and find the biggest common factor number .

Step-1: Prime Factorization of 30800

Prime factors of 30800 are 2, 5, 7, 11. Prime factorization of 30800 in exponential form is:

30800 = 2⁴ × 5² × 7¹ × 11¹

Step-2: 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-3: Factors of 30800

List of positive integer factors of 30800 that divides 30800 without a remainder.

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 20, 22, 25, 28, 35, 40, 44, 50, 55, 56, 70, 77, 80, 88, 100, 110, 112, 140, 154, 175, 176, 200, 220, 275, 280, 308, 350, 385, 400, 440, 550, 560, 616, 700, 770, 880, 1100, 1232, 1400, 1540, 1925, 2200, 2800, 3080, 3850, 4400, 6160, 7700, 15400

Step-4: Factors of 30816

List of positive integer factors of 30816 that divides 30800 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30800 and 30816. The biggest common factor number is the GCF number.
So the greatest common factor 30800 and 30816 is 16.

Also check out the Least Common Multiple of 30800 and 30816