What is the Greatest Common Factor of 13758 and 13770?

Greatest common factor (GCF) of 13758 and 13770 is 6.

GCF(13758,13770) = 6

We will now calculate the prime factors of 13758 and 13770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13758 and 13770.

How to find the GCF of 13758 and 13770?

We will first find the prime factorization of 13758 and 13770. After we will calculate the factors of 13758 and 13770 and find the biggest common factor number .

Step-1: Prime Factorization of 13758

Prime factors of 13758 are 2, 3, 2293. Prime factorization of 13758 in exponential form is:

13758 = 2¹ × 3¹ × 2293¹

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 13758

List of positive integer factors of 13758 that divides 13758 without a remainder.

1, 2, 3, 6, 2293, 4586, 6879

Step-4: Factors of 13770

List of positive integer factors of 13770 that divides 13758 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 13758 and 13770. The biggest common factor number is the GCF number.
So the greatest common factor 13758 and 13770 is 6.

Also check out the Least Common Multiple of 13758 and 13770