What is the Greatest Common Factor of 17739 and 17745?

Greatest common factor (GCF) of 17739 and 17745 is 3.

GCF(17739,17745) = 3

We will now calculate the prime factors of 17739 and 17745, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17739 and 17745.

How to find the GCF of 17739 and 17745?

We will first find the prime factorization of 17739 and 17745. After we will calculate the factors of 17739 and 17745 and find the biggest common factor number .

Step-1: Prime Factorization of 17739

Prime factors of 17739 are 3, 73. Prime factorization of 17739 in exponential form is:

17739 = 3⁵ × 73¹

Step-2: Prime Factorization of 17745

Prime factors of 17745 are 3, 5, 7, 13. Prime factorization of 17745 in exponential form is:

17745 = 3¹ × 5¹ × 7¹ × 13²

Step-3: Factors of 17739

List of positive integer factors of 17739 that divides 17739 without a remainder.

1, 3, 9, 27, 73, 81, 219, 243, 657, 1971, 5913

Step-4: Factors of 17745

List of positive integer factors of 17745 that divides 17739 without a remainder.

1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 169, 195, 273, 455, 507, 845, 1183, 1365, 2535, 3549, 5915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17739 and 17745. The biggest common factor number is the GCF number.
So the greatest common factor 17739 and 17745 is 3.

Also check out the Least Common Multiple of 17739 and 17745