What is the Greatest Common Factor of 13770 and 13776?

Greatest common factor (GCF) of 13770 and 13776 is 6.

GCF(13770,13776) = 6

We will now calculate the prime factors of 13770 and 13776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13770 and 13776.

How to find the GCF of 13770 and 13776?

We will first find the prime factorization of 13770 and 13776. After we will calculate the factors of 13770 and 13776 and find the biggest common factor number .

Step-1: Prime Factorization of 13770

Prime factors of 13770 are 2, 3, 5, 17. Prime factorization of 13770 in exponential form is:

13770 = 2¹ × 3⁴ × 5¹ × 17¹

Step-2: Prime Factorization of 13776

Prime factors of 13776 are 2, 3, 7, 41. Prime factorization of 13776 in exponential form is:

13776 = 2⁴ × 3¹ × 7¹ × 41¹

Step-3: Factors of 13770

List of positive integer factors of 13770 that divides 13770 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 27, 30, 34, 45, 51, 54, 81, 85, 90, 102, 135, 153, 162, 170, 255, 270, 306, 405, 459, 510, 765, 810, 918, 1377, 1530, 2295, 2754, 4590, 6885

Step-4: Factors of 13776

List of positive integer factors of 13776 that divides 13770 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 41, 42, 48, 56, 82, 84, 112, 123, 164, 168, 246, 287, 328, 336, 492, 574, 656, 861, 984, 1148, 1722, 1968, 2296, 3444, 4592, 6888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13770 and 13776. The biggest common factor number is the GCF number.
So the greatest common factor 13770 and 13776 is 6.

Also check out the Least Common Multiple of 13770 and 13776