What is the Greatest Common Factor of 31728 and 31746?

Greatest common factor (GCF) of 31728 and 31746 is 6.

GCF(31728,31746) = 6

We will now calculate the prime factors of 31728 and 31746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31728 and 31746.

How to find the GCF of 31728 and 31746?

We will first find the prime factorization of 31728 and 31746. After we will calculate the factors of 31728 and 31746 and find the biggest common factor number .

Step-1: Prime Factorization of 31728

Prime factors of 31728 are 2, 3, 661. Prime factorization of 31728 in exponential form is:

31728 = 2⁴ × 3¹ × 661¹

Step-2: Prime Factorization of 31746

Prime factors of 31746 are 2, 3, 11, 13, 37. Prime factorization of 31746 in exponential form is:

31746 = 2¹ × 3¹ × 11¹ × 13¹ × 37¹

Step-3: Factors of 31728

List of positive integer factors of 31728 that divides 31728 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 661, 1322, 1983, 2644, 3966, 5288, 7932, 10576, 15864

Step-4: Factors of 31746

List of positive integer factors of 31746 that divides 31728 without a remainder.

1, 2, 3, 6, 11, 13, 22, 26, 33, 37, 39, 66, 74, 78, 111, 143, 222, 286, 407, 429, 481, 814, 858, 962, 1221, 1443, 2442, 2886, 5291, 10582, 15873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31728 and 31746. The biggest common factor number is the GCF number.
So the greatest common factor 31728 and 31746 is 6.

Also check out the Least Common Multiple of 31728 and 31746