What is the Greatest Common Factor of 6705 and 6717?

Greatest common factor (GCF) of 6705 and 6717 is 3.

GCF(6705,6717) = 3

We will now calculate the prime factors of 6705 and 6717, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6705 and 6717.

How to find the GCF of 6705 and 6717?

We will first find the prime factorization of 6705 and 6717. After we will calculate the factors of 6705 and 6717 and find the biggest common factor number .

Step-1: Prime Factorization of 6705

Prime factors of 6705 are 3, 5, 149. Prime factorization of 6705 in exponential form is:

6705 = 3² × 5¹ × 149¹

Step-2: Prime Factorization of 6717

Prime factors of 6717 are 3, 2239. Prime factorization of 6717 in exponential form is:

6717 = 3¹ × 2239¹

Step-3: Factors of 6705

List of positive integer factors of 6705 that divides 6705 without a remainder.

1, 3, 5, 9, 15, 45, 149, 447, 745, 1341, 2235

Step-4: Factors of 6717

List of positive integer factors of 6717 that divides 6705 without a remainder.

1, 3, 2239

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6705 and 6717. The biggest common factor number is the GCF number.
So the greatest common factor 6705 and 6717 is 3.

Also check out the Least Common Multiple of 6705 and 6717