What is the Greatest Common Factor of 13770 and 13785?

Greatest common factor (GCF) of 13770 and 13785 is 15.

GCF(13770,13785) = 15

We will now calculate the prime factors of 13770 and 13785, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13770 and 13785.

How to find the GCF of 13770 and 13785?

We will first find the prime factorization of 13770 and 13785. After we will calculate the factors of 13770 and 13785 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 13785

Prime factors of 13785 are 3, 5, 919. Prime factorization of 13785 in exponential form is:

13785 = 3¹ × 5¹ × 919¹

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 13785

List of positive integer factors of 13785 that divides 13770 without a remainder.

1, 3, 5, 15, 919, 2757, 4595

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13770 and 13785. The biggest common factor number is the GCF number.
So the greatest common factor 13770 and 13785 is 15.

Also check out the Least Common Multiple of 13770 and 13785