What is the Greatest Common Factor of 30864 and 30870?

Greatest common factor (GCF) of 30864 and 30870 is 6.

GCF(30864,30870) = 6

We will now calculate the prime factors of 30864 and 30870, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30864 and 30870.

How to find the GCF of 30864 and 30870?

We will first find the prime factorization of 30864 and 30870. After we will calculate the factors of 30864 and 30870 and find the biggest common factor number .

Step-1: Prime Factorization of 30864

Prime factors of 30864 are 2, 3, 643. Prime factorization of 30864 in exponential form is:

30864 = 2⁴ × 3¹ × 643¹

Step-2: 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-3: Factors of 30864

List of positive integer factors of 30864 that divides 30864 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 643, 1286, 1929, 2572, 3858, 5144, 7716, 10288, 15432

Step-4: Factors of 30870

List of positive integer factors of 30870 that divides 30864 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30864 and 30870. The biggest common factor number is the GCF number.
So the greatest common factor 30864 and 30870 is 6.

Also check out the Least Common Multiple of 30864 and 30870