What is the Greatest Common Factor of 6849 and 6864?

Greatest common factor (GCF) of 6849 and 6864 is 3.

GCF(6849,6864) = 3

We will now calculate the prime factors of 6849 and 6864, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6849 and 6864.

How to find the GCF of 6849 and 6864?

We will first find the prime factorization of 6849 and 6864. After we will calculate the factors of 6849 and 6864 and find the biggest common factor number .

Step-1: Prime Factorization of 6849

Prime factors of 6849 are 3, 761. Prime factorization of 6849 in exponential form is:

6849 = 3² × 761¹

Step-2: Prime Factorization of 6864

Prime factors of 6864 are 2, 3, 11, 13. Prime factorization of 6864 in exponential form is:

6864 = 2⁴ × 3¹ × 11¹ × 13¹

Step-3: Factors of 6849

List of positive integer factors of 6849 that divides 6849 without a remainder.

1, 3, 9, 761, 2283

Step-4: Factors of 6864

List of positive integer factors of 6864 that divides 6849 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 33, 39, 44, 48, 52, 66, 78, 88, 104, 132, 143, 156, 176, 208, 264, 286, 312, 429, 528, 572, 624, 858, 1144, 1716, 2288, 3432

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6849 and 6864. The biggest common factor number is the GCF number.
So the greatest common factor 6849 and 6864 is 3.

Also check out the Least Common Multiple of 6849 and 6864