What is the Greatest Common Factor of 705 and 723?

Greatest common factor (GCF) of 705 and 723 is 3.

GCF(705,723) = 3

We will now calculate the prime factors of 705 and 723, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 705 and 723.

How to find the GCF of 705 and 723?

We will first find the prime factorization of 705 and 723. After we will calculate the factors of 705 and 723 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 723

Prime factors of 723 are 3, 241. Prime factorization of 723 in exponential form is:

723 = 3¹ × 241¹

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 723

List of positive integer factors of 723 that divides 705 without a remainder.

1, 3, 241

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 705 and 723. The biggest common factor number is the GCF number.
So the greatest common factor 705 and 723 is 3.

Also check out the Least Common Multiple of 705 and 723