What is the Greatest Common Factor of 17738 and 17745?

Greatest common factor (GCF) of 17738 and 17745 is 7.

GCF(17738,17745) = 7

We will now calculate the prime factors of 17738 and 17745, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17738 and 17745.

How to find the GCF of 17738 and 17745?

We will first find the prime factorization of 17738 and 17745. After we will calculate the factors of 17738 and 17745 and find the biggest common factor number .

Step-1: Prime Factorization of 17738

Prime factors of 17738 are 2, 7, 181. Prime factorization of 17738 in exponential form is:

17738 = 2¹ × 7² × 181¹

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 17738

List of positive integer factors of 17738 that divides 17738 without a remainder.

1, 2, 7, 14, 49, 98, 181, 362, 1267, 2534, 8869

Step-4: Factors of 17745

List of positive integer factors of 17745 that divides 17738 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 17738 and 17745. The biggest common factor number is the GCF number.
So the greatest common factor 17738 and 17745 is 7.

Also check out the Least Common Multiple of 17738 and 17745