What is the Greatest Common Factor of 705 and 717?

Greatest common factor (GCF) of 705 and 717 is 3.

GCF(705,717) = 3

We will now calculate the prime factors of 705 and 717, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 705 and 717.

How to find the GCF of 705 and 717?

We will first find the prime factorization of 705 and 717. After we will calculate the factors of 705 and 717 and find the biggest common factor number .

Step-1: Prime Factorization of 705

Prime factors of 705 are 3, 5, 47. Prime factorization of 705 in exponential form is:

705 = 3¹ × 5¹ × 47¹

Step-2: Prime Factorization of 717

Prime factors of 717 are 3, 239. Prime factorization of 717 in exponential form is:

717 = 3¹ × 239¹

Step-3: Factors of 705

List of positive integer factors of 705 that divides 705 without a remainder.

1, 3, 5, 15, 47, 141, 235

Step-4: Factors of 717

List of positive integer factors of 717 that divides 705 without a remainder.

1, 3, 239

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 705 and 717. The biggest common factor number is the GCF number.
So the greatest common factor 705 and 717 is 3.

Also check out the Least Common Multiple of 705 and 717