What is the Greatest Common Factor of 2709 and 2723?

Greatest common factor (GCF) of 2709 and 2723 is 7.

GCF(2709,2723) = 7

We will now calculate the prime factors of 2709 and 2723, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2709 and 2723.

How to find the GCF of 2709 and 2723?

We will first find the prime factorization of 2709 and 2723. After we will calculate the factors of 2709 and 2723 and find the biggest common factor number .

Step-1: Prime Factorization of 2709

Prime factors of 2709 are 3, 7, 43. Prime factorization of 2709 in exponential form is:

2709 = 3² × 7¹ × 43¹

Step-2: Prime Factorization of 2723

Prime factors of 2723 are 7, 389. Prime factorization of 2723 in exponential form is:

2723 = 7¹ × 389¹

Step-3: Factors of 2709

List of positive integer factors of 2709 that divides 2709 without a remainder.

1, 3, 7, 9, 21, 43, 63, 129, 301, 387, 903

Step-4: Factors of 2723

List of positive integer factors of 2723 that divides 2709 without a remainder.

1, 7, 389

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2709 and 2723. The biggest common factor number is the GCF number.
So the greatest common factor 2709 and 2723 is 7.

Also check out the Least Common Multiple of 2709 and 2723