What is the Greatest Common Factor of 13755 and 13770?

Greatest common factor (GCF) of 13755 and 13770 is 15.

GCF(13755,13770) = 15

We will now calculate the prime factors of 13755 and 13770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13755 and 13770.

How to find the GCF of 13755 and 13770?

We will first find the prime factorization of 13755 and 13770. After we will calculate the factors of 13755 and 13770 and find the biggest common factor number .

Step-1: 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-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 13755

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

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

Step-4: Factors of 13770

List of positive integer factors of 13770 that divides 13755 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 13755 and 13770. The biggest common factor number is the GCF number.
So the greatest common factor 13755 and 13770 is 15.

Also check out the Least Common Multiple of 13755 and 13770