What is the Greatest Common Factor of 5709 and 5724?

Greatest common factor (GCF) of 5709 and 5724 is 3.

GCF(5709,5724) = 3

We will now calculate the prime factors of 5709 and 5724, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5709 and 5724.

How to find the GCF of 5709 and 5724?

We will first find the prime factorization of 5709 and 5724. After we will calculate the factors of 5709 and 5724 and find the biggest common factor number .

Step-1: Prime Factorization of 5709

Prime factors of 5709 are 3, 11, 173. Prime factorization of 5709 in exponential form is:

5709 = 3¹ × 11¹ × 173¹

Step-2: Prime Factorization of 5724

Prime factors of 5724 are 2, 3, 53. Prime factorization of 5724 in exponential form is:

5724 = 2² × 3³ × 53¹

Step-3: Factors of 5709

List of positive integer factors of 5709 that divides 5709 without a remainder.

1, 3, 11, 33, 173, 519, 1903

Step-4: Factors of 5724

List of positive integer factors of 5724 that divides 5709 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 53, 54, 106, 108, 159, 212, 318, 477, 636, 954, 1431, 1908, 2862

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5709 and 5724. The biggest common factor number is the GCF number.
So the greatest common factor 5709 and 5724 is 3.

Also check out the Least Common Multiple of 5709 and 5724