What is the Greatest Common Factor of 17745 and 17757?

Greatest common factor (GCF) of 17745 and 17757 is 3.

GCF(17745,17757) = 3

We will now calculate the prime factors of 17745 and 17757, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17745 and 17757.

How to find the GCF of 17745 and 17757?

We will first find the prime factorization of 17745 and 17757. After we will calculate the factors of 17745 and 17757 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 17757

Prime factors of 17757 are 3, 1973. Prime factorization of 17757 in exponential form is:

17757 = 3² × 1973¹

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 17757

List of positive integer factors of 17757 that divides 17745 without a remainder.

1, 3, 9, 1973, 5919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17745 and 17757. The biggest common factor number is the GCF number.
So the greatest common factor 17745 and 17757 is 3.

Also check out the Least Common Multiple of 17745 and 17757