What is the Greatest Common Factor of 35712 and 35728?

Greatest common factor (GCF) of 35712 and 35728 is 16.

GCF(35712,35728) = 16

We will now calculate the prime factors of 35712 and 35728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35712 and 35728.

How to find the GCF of 35712 and 35728?

We will first find the prime factorization of 35712 and 35728. After we will calculate the factors of 35712 and 35728 and find the biggest common factor number .

Step-1: Prime Factorization of 35712

Prime factors of 35712 are 2, 3, 31. Prime factorization of 35712 in exponential form is:

35712 = 2⁷ × 3² × 31¹

Step-2: 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-3: Factors of 35712

List of positive integer factors of 35712 that divides 35712 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 31, 32, 36, 48, 62, 64, 72, 93, 96, 124, 128, 144, 186, 192, 248, 279, 288, 372, 384, 496, 558, 576, 744, 992, 1116, 1152, 1488, 1984, 2232, 2976, 3968, 4464, 5952, 8928, 11904, 17856

Step-4: Factors of 35728

List of positive integer factors of 35728 that divides 35712 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35712 and 35728. The biggest common factor number is the GCF number.
So the greatest common factor 35712 and 35728 is 16.

Also check out the Least Common Multiple of 35712 and 35728