What is the Greatest Common Factor of 18105 and 18122?

Greatest common factor (GCF) of 18105 and 18122 is 17.

GCF(18105,18122) = 17

We will now calculate the prime factors of 18105 and 18122, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18105 and 18122.

How to find the GCF of 18105 and 18122?

We will first find the prime factorization of 18105 and 18122. After we will calculate the factors of 18105 and 18122 and find the biggest common factor number .

Step-1: Prime Factorization of 18105

Prime factors of 18105 are 3, 5, 17, 71. Prime factorization of 18105 in exponential form is:

18105 = 3¹ × 5¹ × 17¹ × 71¹

Step-2: Prime Factorization of 18122

Prime factors of 18122 are 2, 13, 17, 41. Prime factorization of 18122 in exponential form is:

18122 = 2¹ × 13¹ × 17¹ × 41¹

Step-3: Factors of 18105

List of positive integer factors of 18105 that divides 18105 without a remainder.

1, 3, 5, 15, 17, 51, 71, 85, 213, 255, 355, 1065, 1207, 3621, 6035

Step-4: Factors of 18122

List of positive integer factors of 18122 that divides 18105 without a remainder.

1, 2, 13, 17, 26, 34, 41, 82, 221, 442, 533, 697, 1066, 1394, 9061

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18105 and 18122. The biggest common factor number is the GCF number.
So the greatest common factor 18105 and 18122 is 17.

Also check out the Least Common Multiple of 18105 and 18122