What is the Greatest Common Factor of 35728 and 35734?

Greatest common factor (GCF) of 35728 and 35734 is 2.

GCF(35728,35734) = 2

We will now calculate the prime factors of 35728 and 35734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35728 and 35734.

How to find the GCF of 35728 and 35734?

We will first find the prime factorization of 35728 and 35734. After we will calculate the factors of 35728 and 35734 and find the biggest common factor number .

Step-1: Prime Factorization of 35728

Prime factors of 35728 are 2, 7, 11, 29. Prime factorization of 35728 in exponential form is:

35728 = 2⁴ × 7¹ × 11¹ × 29¹

Step-2: Prime Factorization of 35734

Prime factors of 35734 are 2, 17, 1051. Prime factorization of 35734 in exponential form is:

35734 = 2¹ × 17¹ × 1051¹

Step-3: Factors of 35728

List of positive integer factors of 35728 that divides 35728 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 29, 44, 56, 58, 77, 88, 112, 116, 154, 176, 203, 232, 308, 319, 406, 464, 616, 638, 812, 1232, 1276, 1624, 2233, 2552, 3248, 4466, 5104, 8932, 17864

Step-4: Factors of 35734

List of positive integer factors of 35734 that divides 35728 without a remainder.

1, 2, 17, 34, 1051, 2102, 17867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35728 and 35734. The biggest common factor number is the GCF number.
So the greatest common factor 35728 and 35734 is 2.

Also check out the Least Common Multiple of 35728 and 35734