What is the Greatest Common Factor of 35696 and 35712?

Greatest common factor (GCF) of 35696 and 35712 is 16.

GCF(35696,35712) = 16

We will now calculate the prime factors of 35696 and 35712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35696 and 35712.

How to find the GCF of 35696 and 35712?

We will first find the prime factorization of 35696 and 35712. After we will calculate the factors of 35696 and 35712 and find the biggest common factor number .

Step-1: Prime Factorization of 35696

Prime factors of 35696 are 2, 23, 97. Prime factorization of 35696 in exponential form is:

35696 = 2⁴ × 23¹ × 97¹

Step-2: 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-3: Factors of 35696

List of positive integer factors of 35696 that divides 35696 without a remainder.

1, 2, 4, 8, 16, 23, 46, 92, 97, 184, 194, 368, 388, 776, 1552, 2231, 4462, 8924, 17848

Step-4: Factors of 35712

List of positive integer factors of 35712 that divides 35696 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35696 and 35712. The biggest common factor number is the GCF number.
So the greatest common factor 35696 and 35712 is 16.

Also check out the Least Common Multiple of 35696 and 35712