What is the Greatest Common Factor of 30880 and 30900?

Greatest common factor (GCF) of 30880 and 30900 is 20.

GCF(30880,30900) = 20

We will now calculate the prime factors of 30880 and 30900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30880 and 30900.

How to find the GCF of 30880 and 30900?

We will first find the prime factorization of 30880 and 30900. After we will calculate the factors of 30880 and 30900 and find the biggest common factor number .

Step-1: Prime Factorization of 30880

Prime factors of 30880 are 2, 5, 193. Prime factorization of 30880 in exponential form is:

30880 = 2⁵ × 5¹ × 193¹

Step-2: Prime Factorization of 30900

Prime factors of 30900 are 2, 3, 5, 103. Prime factorization of 30900 in exponential form is:

30900 = 2² × 3¹ × 5² × 103¹

Step-3: Factors of 30880

List of positive integer factors of 30880 that divides 30880 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 193, 386, 772, 965, 1544, 1930, 3088, 3860, 6176, 7720, 15440

Step-4: Factors of 30900

List of positive integer factors of 30900 that divides 30880 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 103, 150, 206, 300, 309, 412, 515, 618, 1030, 1236, 1545, 2060, 2575, 3090, 5150, 6180, 7725, 10300, 15450

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30880 and 30900. The biggest common factor number is the GCF number.
So the greatest common factor 30880 and 30900 is 20.

Also check out the Least Common Multiple of 30880 and 30900