What is the Greatest Common Factor of 34728 and 34742?

Greatest common factor (GCF) of 34728 and 34742 is 2.

GCF(34728,34742) = 2

We will now calculate the prime factors of 34728 and 34742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34728 and 34742.

How to find the GCF of 34728 and 34742?

We will first find the prime factorization of 34728 and 34742. After we will calculate the factors of 34728 and 34742 and find the biggest common factor number .

Step-1: Prime Factorization of 34728

Prime factors of 34728 are 2, 3, 1447. Prime factorization of 34728 in exponential form is:

34728 = 2³ × 3¹ × 1447¹

Step-2: Prime Factorization of 34742

Prime factors of 34742 are 2, 29, 599. Prime factorization of 34742 in exponential form is:

34742 = 2¹ × 29¹ × 599¹

Step-3: Factors of 34728

List of positive integer factors of 34728 that divides 34728 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1447, 2894, 4341, 5788, 8682, 11576, 17364

Step-4: Factors of 34742

List of positive integer factors of 34742 that divides 34728 without a remainder.

1, 2, 29, 58, 599, 1198, 17371

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34728 and 34742. The biggest common factor number is the GCF number.
So the greatest common factor 34728 and 34742 is 2.

Also check out the Least Common Multiple of 34728 and 34742