What is the Greatest Common Factor of 17205 and 17223?

Greatest common factor (GCF) of 17205 and 17223 is 3.

GCF(17205,17223) = 3

We will now calculate the prime factors of 17205 and 17223, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17205 and 17223.

How to find the GCF of 17205 and 17223?

We will first find the prime factorization of 17205 and 17223. After we will calculate the factors of 17205 and 17223 and find the biggest common factor number .

Step-1: Prime Factorization of 17205

Prime factors of 17205 are 3, 5, 31, 37. Prime factorization of 17205 in exponential form is:

17205 = 3¹ × 5¹ × 31¹ × 37¹

Step-2: Prime Factorization of 17223

Prime factors of 17223 are 3, 5741. Prime factorization of 17223 in exponential form is:

17223 = 3¹ × 5741¹

Step-3: Factors of 17205

List of positive integer factors of 17205 that divides 17205 without a remainder.

1, 3, 5, 15, 31, 37, 93, 111, 155, 185, 465, 555, 1147, 3441, 5735

Step-4: Factors of 17223

List of positive integer factors of 17223 that divides 17205 without a remainder.

1, 3, 5741

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17205 and 17223. The biggest common factor number is the GCF number.
So the greatest common factor 17205 and 17223 is 3.

Also check out the Least Common Multiple of 17205 and 17223