What is the Greatest Common Factor of 13731 and 13740?

Greatest common factor (GCF) of 13731 and 13740 is 3.

GCF(13731,13740) = 3

We will now calculate the prime factors of 13731 and 13740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13731 and 13740.

How to find the GCF of 13731 and 13740?

We will first find the prime factorization of 13731 and 13740. After we will calculate the factors of 13731 and 13740 and find the biggest common factor number .

Step-1: Prime Factorization of 13731

Prime factors of 13731 are 3, 23, 199. Prime factorization of 13731 in exponential form is:

13731 = 3¹ × 23¹ × 199¹

Step-2: Prime Factorization of 13740

Prime factors of 13740 are 2, 3, 5, 229. Prime factorization of 13740 in exponential form is:

13740 = 2² × 3¹ × 5¹ × 229¹

Step-3: Factors of 13731

List of positive integer factors of 13731 that divides 13731 without a remainder.

1, 3, 23, 69, 199, 597, 4577

Step-4: Factors of 13740

List of positive integer factors of 13740 that divides 13731 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 229, 458, 687, 916, 1145, 1374, 2290, 2748, 3435, 4580, 6870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13731 and 13740. The biggest common factor number is the GCF number.
So the greatest common factor 13731 and 13740 is 3.

Also check out the Least Common Multiple of 13731 and 13740