What is the Greatest Common Factor of 13740 and 13755?

Greatest common factor (GCF) of 13740 and 13755 is 15.

GCF(13740,13755) = 15

We will now calculate the prime factors of 13740 and 13755, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13740 and 13755.

How to find the GCF of 13740 and 13755?

We will first find the prime factorization of 13740 and 13755. After we will calculate the factors of 13740 and 13755 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13755

Prime factors of 13755 are 3, 5, 7, 131. Prime factorization of 13755 in exponential form is:

13755 = 3¹ × 5¹ × 7¹ × 131¹

Step-3: Factors of 13740

List of positive integer factors of 13740 that divides 13740 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

Step-4: Factors of 13755

List of positive integer factors of 13755 that divides 13740 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 131, 393, 655, 917, 1965, 2751, 4585

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13740 and 13755. The biggest common factor number is the GCF number.
So the greatest common factor 13740 and 13755 is 15.

Also check out the Least Common Multiple of 13740 and 13755