What is the Greatest Common Factor of 6705 and 6714?

Greatest common factor (GCF) of 6705 and 6714 is 9.

GCF(6705,6714) = 9

We will now calculate the prime factors of 6705 and 6714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6705 and 6714.

How to find the GCF of 6705 and 6714?

We will first find the prime factorization of 6705 and 6714. After we will calculate the factors of 6705 and 6714 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 6714

Prime factors of 6714 are 2, 3, 373. Prime factorization of 6714 in exponential form is:

6714 = 2¹ × 3² × 373¹

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 6714

List of positive integer factors of 6714 that divides 6705 without a remainder.

1, 2, 3, 6, 9, 18, 373, 746, 1119, 2238, 3357

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6705 and 6714. The biggest common factor number is the GCF number.
So the greatest common factor 6705 and 6714 is 9.

Also check out the Least Common Multiple of 6705 and 6714