What is the Greatest Common Factor of 18105 and 18114?

Greatest common factor (GCF) of 18105 and 18114 is 3.

GCF(18105,18114) = 3

We will now calculate the prime factors of 18105 and 18114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18105 and 18114.

How to find the GCF of 18105 and 18114?

We will first find the prime factorization of 18105 and 18114. After we will calculate the factors of 18105 and 18114 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 18114

Prime factors of 18114 are 2, 3, 3019. Prime factorization of 18114 in exponential form is:

18114 = 2¹ × 3¹ × 3019¹

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 18114

List of positive integer factors of 18114 that divides 18105 without a remainder.

1, 2, 3, 6, 3019, 6038, 9057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18105 and 18114. The biggest common factor number is the GCF number.
So the greatest common factor 18105 and 18114 is 3.

Also check out the Least Common Multiple of 18105 and 18114