What is the Greatest Common Factor of 30800 and 30808?

Greatest common factor (GCF) of 30800 and 30808 is 8.

GCF(30800,30808) = 8

We will now calculate the prime factors of 30800 and 30808, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30800 and 30808.

How to find the GCF of 30800 and 30808?

We will first find the prime factorization of 30800 and 30808. After we will calculate the factors of 30800 and 30808 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 30808

Prime factors of 30808 are 2, 3851. Prime factorization of 30808 in exponential form is:

30808 = 2³ × 3851¹

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 30808

List of positive integer factors of 30808 that divides 30800 without a remainder.

1, 2, 4, 8, 3851, 7702, 15404

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30800 and 30808. The biggest common factor number is the GCF number.
So the greatest common factor 30800 and 30808 is 8.

Also check out the Least Common Multiple of 30800 and 30808