What is the Greatest Common Factor of 30800 and 30820?

Greatest common factor (GCF) of 30800 and 30820 is 20.

GCF(30800,30820) = 20

We will now calculate the prime factors of 30800 and 30820, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30800 and 30820.

How to find the GCF of 30800 and 30820?

We will first find the prime factorization of 30800 and 30820. After we will calculate the factors of 30800 and 30820 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 30820

Prime factors of 30820 are 2, 5, 23, 67. Prime factorization of 30820 in exponential form is:

30820 = 2² × 5¹ × 23¹ × 67¹

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 30820

List of positive integer factors of 30820 that divides 30800 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 67, 92, 115, 134, 230, 268, 335, 460, 670, 1340, 1541, 3082, 6164, 7705, 15410

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30800 and 30820. The biggest common factor number is the GCF number.
So the greatest common factor 30800 and 30820 is 20.

Also check out the Least Common Multiple of 30800 and 30820