What is the Greatest Common Factor of 13761 and 13770?

Greatest common factor (GCF) of 13761 and 13770 is 9.

GCF(13761,13770) = 9

We will now calculate the prime factors of 13761 and 13770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13761 and 13770.

How to find the GCF of 13761 and 13770?

We will first find the prime factorization of 13761 and 13770. After we will calculate the factors of 13761 and 13770 and find the biggest common factor number .

Step-1: Prime Factorization of 13761

Prime factors of 13761 are 3, 11, 139. Prime factorization of 13761 in exponential form is:

13761 = 3² × 11¹ × 139¹

Step-2: 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-3: Factors of 13761

List of positive integer factors of 13761 that divides 13761 without a remainder.

1, 3, 9, 11, 33, 99, 139, 417, 1251, 1529, 4587

Step-4: Factors of 13770

List of positive integer factors of 13770 that divides 13761 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13761 and 13770. The biggest common factor number is the GCF number.
So the greatest common factor 13761 and 13770 is 9.

Also check out the Least Common Multiple of 13761 and 13770