What is the Greatest Common Factor of 31733 and 31746?

Greatest common factor (GCF) of 31733 and 31746 is 13.

GCF(31733,31746) = 13

We will now calculate the prime factors of 31733 and 31746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31733 and 31746.

How to find the GCF of 31733 and 31746?

We will first find the prime factorization of 31733 and 31746. After we will calculate the factors of 31733 and 31746 and find the biggest common factor number .

Step-1: Prime Factorization of 31733

Prime factors of 31733 are 13, 2441. Prime factorization of 31733 in exponential form is:

31733 = 13¹ × 2441¹

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 31733

List of positive integer factors of 31733 that divides 31733 without a remainder.

1, 13, 2441

Step-4: Factors of 31746

List of positive integer factors of 31746 that divides 31733 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 31733 and 31746. The biggest common factor number is the GCF number.
So the greatest common factor 31733 and 31746 is 13.

Also check out the Least Common Multiple of 31733 and 31746