What is the Greatest Common Factor of 30870 and 30880?

Greatest common factor (GCF) of 30870 and 30880 is 10.

GCF(30870,30880) = 10

We will now calculate the prime factors of 30870 and 30880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30870 and 30880.

How to find the GCF of 30870 and 30880?

We will first find the prime factorization of 30870 and 30880. After we will calculate the factors of 30870 and 30880 and find the biggest common factor number .

Step-1: Prime Factorization of 30870

Prime factors of 30870 are 2, 3, 5, 7. Prime factorization of 30870 in exponential form is:

30870 = 2¹ × 3² × 5¹ × 7³

Step-2: 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-3: Factors of 30870

List of positive integer factors of 30870 that divides 30870 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 49, 63, 70, 90, 98, 105, 126, 147, 210, 245, 294, 315, 343, 441, 490, 630, 686, 735, 882, 1029, 1470, 1715, 2058, 2205, 3087, 3430, 4410, 5145, 6174, 10290, 15435

Step-4: Factors of 30880

List of positive integer factors of 30880 that divides 30870 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30870 and 30880. The biggest common factor number is the GCF number.
So the greatest common factor 30870 and 30880 is 10.

Also check out the Least Common Multiple of 30870 and 30880