What is the Greatest Common Factor of 17745 and 17754?

Greatest common factor (GCF) of 17745 and 17754 is 3.

GCF(17745,17754) = 3

We will now calculate the prime factors of 17745 and 17754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17745 and 17754.

How to find the GCF of 17745 and 17754?

We will first find the prime factorization of 17745 and 17754. After we will calculate the factors of 17745 and 17754 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 17754

Prime factors of 17754 are 2, 3, 11, 269. Prime factorization of 17754 in exponential form is:

17754 = 2¹ × 3¹ × 11¹ × 269¹

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 17754

List of positive integer factors of 17754 that divides 17745 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 269, 538, 807, 1614, 2959, 5918, 8877

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17745 and 17754. The biggest common factor number is the GCF number.
So the greatest common factor 17745 and 17754 is 3.

Also check out the Least Common Multiple of 17745 and 17754