What is the Greatest Common Factor of 75724 and 75742?

Greatest common factor (GCF) of 75724 and 75742 is 2.

GCF(75724,75742) = 2

We will now calculate the prime factors of 75724 and 75742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75724 and 75742.

How to find the GCF of 75724 and 75742?

We will first find the prime factorization of 75724 and 75742. After we will calculate the factors of 75724 and 75742 and find the biggest common factor number .

Step-1: Prime Factorization of 75724

Prime factors of 75724 are 2, 11, 1721. Prime factorization of 75724 in exponential form is:

75724 = 2² × 11¹ × 1721¹

Step-2: Prime Factorization of 75742

Prime factors of 75742 are 2, 37871. Prime factorization of 75742 in exponential form is:

75742 = 2¹ × 37871¹

Step-3: Factors of 75724

List of positive integer factors of 75724 that divides 75724 without a remainder.

1, 2, 4, 11, 22, 44, 1721, 3442, 6884, 18931, 37862

Step-4: Factors of 75742

List of positive integer factors of 75742 that divides 75724 without a remainder.

1, 2, 37871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75724 and 75742. The biggest common factor number is the GCF number.
So the greatest common factor 75724 and 75742 is 2.

Also check out the Least Common Multiple of 75724 and 75742