What is the Greatest Common Factor of 30849 and 30864?

Greatest common factor (GCF) of 30849 and 30864 is 3.

GCF(30849,30864) = 3

We will now calculate the prime factors of 30849 and 30864, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30849 and 30864.

How to find the GCF of 30849 and 30864?

We will first find the prime factorization of 30849 and 30864. After we will calculate the factors of 30849 and 30864 and find the biggest common factor number .

Step-1: Prime Factorization of 30849

Prime factors of 30849 are 3, 7, 13, 113. Prime factorization of 30849 in exponential form is:

30849 = 3¹ × 7¹ × 13¹ × 113¹

Step-2: 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-3: Factors of 30849

List of positive integer factors of 30849 that divides 30849 without a remainder.

1, 3, 7, 13, 21, 39, 91, 113, 273, 339, 791, 1469, 2373, 4407, 10283

Step-4: Factors of 30864

List of positive integer factors of 30864 that divides 30849 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30849 and 30864. The biggest common factor number is the GCF number.
So the greatest common factor 30849 and 30864 is 3.

Also check out the Least Common Multiple of 30849 and 30864