What is the Greatest Common Factor of 5728 and 5742?

Greatest common factor (GCF) of 5728 and 5742 is 2.

GCF(5728,5742) = 2

We will now calculate the prime factors of 5728 and 5742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5728 and 5742.

How to find the GCF of 5728 and 5742?

We will first find the prime factorization of 5728 and 5742. After we will calculate the factors of 5728 and 5742 and find the biggest common factor number .

Step-1: Prime Factorization of 5728

Prime factors of 5728 are 2, 179. Prime factorization of 5728 in exponential form is:

5728 = 2⁵ × 179¹

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 5728

List of positive integer factors of 5728 that divides 5728 without a remainder.

1, 2, 4, 8, 16, 32, 179, 358, 716, 1432, 2864

Step-4: Factors of 5742

List of positive integer factors of 5742 that divides 5728 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 5728 and 5742. The biggest common factor number is the GCF number.
So the greatest common factor 5728 and 5742 is 2.

Also check out the Least Common Multiple of 5728 and 5742