What is the Greatest Common Factor of 17745 and 17751?

Greatest common factor (GCF) of 17745 and 17751 is 3.

GCF(17745,17751) = 3

We will now calculate the prime factors of 17745 and 17751, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17745 and 17751.

How to find the GCF of 17745 and 17751?

We will first find the prime factorization of 17745 and 17751. After we will calculate the factors of 17745 and 17751 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 17751

Prime factors of 17751 are 3, 61, 97. Prime factorization of 17751 in exponential form is:

17751 = 3¹ × 61¹ × 97¹

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 17751

List of positive integer factors of 17751 that divides 17745 without a remainder.

1, 3, 61, 97, 183, 291, 5917

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17745 and 17751. The biggest common factor number is the GCF number.
So the greatest common factor 17745 and 17751 is 3.

Also check out the Least Common Multiple of 17745 and 17751