What is the Greatest Common Factor of 708 and 723?

Greatest common factor (GCF) of 708 and 723 is 3.

GCF(708,723) = 3

We will now calculate the prime factors of 708 and 723, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 708 and 723.

How to find the GCF of 708 and 723?

We will first find the prime factorization of 708 and 723. After we will calculate the factors of 708 and 723 and find the biggest common factor number .

Step-1: Prime Factorization of 708

Prime factors of 708 are 2, 3, 59. Prime factorization of 708 in exponential form is:

708 = 2² × 3¹ × 59¹

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 708

List of positive integer factors of 708 that divides 708 without a remainder.

1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354

Step-4: Factors of 723

List of positive integer factors of 723 that divides 708 without a remainder.

1, 3, 241

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 708 and 723. The biggest common factor number is the GCF number.
So the greatest common factor 708 and 723 is 3.

Also check out the Least Common Multiple of 708 and 723