What is the Greatest Common Factor of 35728 and 35748?

Greatest common factor (GCF) of 35728 and 35748 is 4.

GCF(35728,35748) = 4

We will now calculate the prime factors of 35728 and 35748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35728 and 35748.

How to find the GCF of 35728 and 35748?

We will first find the prime factorization of 35728 and 35748. After we will calculate the factors of 35728 and 35748 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 35748

Prime factors of 35748 are 2, 3, 331. Prime factorization of 35748 in exponential form is:

35748 = 2² × 3³ × 331¹

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 35748

List of positive integer factors of 35748 that divides 35728 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 331, 662, 993, 1324, 1986, 2979, 3972, 5958, 8937, 11916, 17874

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35728 and 35748. The biggest common factor number is the GCF number.
So the greatest common factor 35728 and 35748 is 4.

Also check out the Least Common Multiple of 35728 and 35748