What is the Greatest Common Factor of 17823 and 17838?

Greatest common factor (GCF) of 17823 and 17838 is 3.

GCF(17823,17838) = 3

We will now calculate the prime factors of 17823 and 17838, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17823 and 17838.

How to find the GCF of 17823 and 17838?

We will first find the prime factorization of 17823 and 17838. After we will calculate the factors of 17823 and 17838 and find the biggest common factor number .

Step-1: Prime Factorization of 17823

Prime factors of 17823 are 3, 13, 457. Prime factorization of 17823 in exponential form is:

17823 = 3¹ × 13¹ × 457¹

Step-2: Prime Factorization of 17838

Prime factors of 17838 are 2, 3, 991. Prime factorization of 17838 in exponential form is:

17838 = 2¹ × 3² × 991¹

Step-3: Factors of 17823

List of positive integer factors of 17823 that divides 17823 without a remainder.

1, 3, 13, 39, 457, 1371, 5941

Step-4: Factors of 17838

List of positive integer factors of 17838 that divides 17823 without a remainder.

1, 2, 3, 6, 9, 18, 991, 1982, 2973, 5946, 8919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17823 and 17838. The biggest common factor number is the GCF number.
So the greatest common factor 17823 and 17838 is 3.

Also check out the Least Common Multiple of 17823 and 17838