What is the Greatest Common Factor of 13761 and 13772?

Greatest common factor (GCF) of 13761 and 13772 is 11.

GCF(13761,13772) = 11

We will now calculate the prime factors of 13761 and 13772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13761 and 13772.

How to find the GCF of 13761 and 13772?

We will first find the prime factorization of 13761 and 13772. After we will calculate the factors of 13761 and 13772 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 13772

Prime factors of 13772 are 2, 11, 313. Prime factorization of 13772 in exponential form is:

13772 = 2² × 11¹ × 313¹

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 13772

List of positive integer factors of 13772 that divides 13761 without a remainder.

1, 2, 4, 11, 22, 44, 313, 626, 1252, 3443, 6886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13761 and 13772. The biggest common factor number is the GCF number.
So the greatest common factor 13761 and 13772 is 11.

Also check out the Least Common Multiple of 13761 and 13772