What is the Greatest Common Factor of 17745 and 17761?

Greatest common factor (GCF) of 17745 and 17761 is 1.

GCF(17745,17761) = 1

We will now calculate the prime factors of 17745 and 17761, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17745 and 17761.

How to find the GCF of 17745 and 17761?

We will first find the prime factorization of 17745 and 17761. After we will calculate the factors of 17745 and 17761 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 17761

Prime factors of 17761 are 17761. Prime factorization of 17761 in exponential form is:

17761 = 17761¹

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 17761

List of positive integer factors of 17761 that divides 17745 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17745 and 17761. The biggest common factor number is the GCF number.
So the greatest common factor 17745 and 17761 is 1.

Also check out the Least Common Multiple of 17745 and 17761