What is the Greatest Common Factor of 17745 and 17755?

Greatest common factor (GCF) of 17745 and 17755 is 5.

GCF(17745,17755) = 5

We will now calculate the prime factors of 17745 and 17755, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17745 and 17755.

How to find the GCF of 17745 and 17755?

We will first find the prime factorization of 17745 and 17755. After we will calculate the factors of 17745 and 17755 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17755

Prime factors of 17755 are 5, 53, 67. Prime factorization of 17755 in exponential form is:

17755 = 5¹ × 53¹ × 67¹

Step-3: Factors of 17745

List of positive integer factors of 17745 that divides 17745 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

Step-4: Factors of 17755

List of positive integer factors of 17755 that divides 17745 without a remainder.

1, 5, 53, 67, 265, 335, 3551

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17745 and 17755. The biggest common factor number is the GCF number.
So the greatest common factor 17745 and 17755 is 5.

Also check out the Least Common Multiple of 17745 and 17755