What is the Greatest Common Factor of 5742 and 5757?

Greatest common factor (GCF) of 5742 and 5757 is 3.

GCF(5742,5757) = 3

We will now calculate the prime factors of 5742 and 5757, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5742 and 5757.

How to find the GCF of 5742 and 5757?

We will first find the prime factorization of 5742 and 5757. After we will calculate the factors of 5742 and 5757 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 5757

Prime factors of 5757 are 3, 19, 101. Prime factorization of 5757 in exponential form is:

5757 = 3¹ × 19¹ × 101¹

Step-3: Factors of 5742

List of positive integer factors of 5742 that divides 5742 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

Step-4: Factors of 5757

List of positive integer factors of 5757 that divides 5742 without a remainder.

1, 3, 19, 57, 101, 303, 1919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5742 and 5757. The biggest common factor number is the GCF number.
So the greatest common factor 5742 and 5757 is 3.

Also check out the Least Common Multiple of 5742 and 5757