What is the Greatest Common Factor of 5724 and 5742?

Greatest common factor (GCF) of 5724 and 5742 is 18.

GCF(5724,5742) = 18

We will now calculate the prime factors of 5724 and 5742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5724 and 5742.

How to find the GCF of 5724 and 5742?

We will first find the prime factorization of 5724 and 5742. After we will calculate the factors of 5724 and 5742 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 5742

Prime factors of 5742 are 2, 3, 11, 29. Prime factorization of 5742 in exponential form is:

5742 = 2¹ × 3² × 11¹ × 29¹

Step-3: Factors of 5724

List of positive integer factors of 5724 that divides 5724 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

Step-4: Factors of 5742

List of positive integer factors of 5742 that divides 5724 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 29, 33, 58, 66, 87, 99, 174, 198, 261, 319, 522, 638, 957, 1914, 2871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5724 and 5742. The biggest common factor number is the GCF number.
So the greatest common factor 5724 and 5742 is 18.

Also check out the Least Common Multiple of 5724 and 5742