What is the Greatest Common Factor of 5733 and 5746?

Greatest common factor (GCF) of 5733 and 5746 is 13.

GCF(5733,5746) = 13

We will now calculate the prime factors of 5733 and 5746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5733 and 5746.

How to find the GCF of 5733 and 5746?

We will first find the prime factorization of 5733 and 5746. After we will calculate the factors of 5733 and 5746 and find the biggest common factor number .

Step-1: Prime Factorization of 5733

Prime factors of 5733 are 3, 7, 13. Prime factorization of 5733 in exponential form is:

5733 = 3² × 7² × 13¹

Step-2: Prime Factorization of 5746

Prime factors of 5746 are 2, 13, 17. Prime factorization of 5746 in exponential form is:

5746 = 2¹ × 13² × 17¹

Step-3: Factors of 5733

List of positive integer factors of 5733 that divides 5733 without a remainder.

1, 3, 7, 9, 13, 21, 39, 49, 63, 91, 117, 147, 273, 441, 637, 819, 1911

Step-4: Factors of 5746

List of positive integer factors of 5746 that divides 5733 without a remainder.

1, 2, 13, 17, 26, 34, 169, 221, 338, 442, 2873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5733 and 5746. The biggest common factor number is the GCF number.
So the greatest common factor 5733 and 5746 is 13.

Also check out the Least Common Multiple of 5733 and 5746