What is the Greatest Common Factor of 35712 and 35730?

Greatest common factor (GCF) of 35712 and 35730 is 18.

GCF(35712,35730) = 18

We will now calculate the prime factors of 35712 and 35730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35712 and 35730.

How to find the GCF of 35712 and 35730?

We will first find the prime factorization of 35712 and 35730. After we will calculate the factors of 35712 and 35730 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 35730

Prime factors of 35730 are 2, 3, 5, 397. Prime factorization of 35730 in exponential form is:

35730 = 2¹ × 3² × 5¹ × 397¹

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 35730

List of positive integer factors of 35730 that divides 35712 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 397, 794, 1191, 1985, 2382, 3573, 3970, 5955, 7146, 11910, 17865

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35712 and 35730. The biggest common factor number is the GCF number.
So the greatest common factor 35712 and 35730 is 18.

Also check out the Least Common Multiple of 35712 and 35730