What is the Greatest Common Factor of 17823 and 17829?

Greatest common factor (GCF) of 17823 and 17829 is 3.

GCF(17823,17829) = 3

We will now calculate the prime factors of 17823 and 17829, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17823 and 17829.

How to find the GCF of 17823 and 17829?

We will first find the prime factorization of 17823 and 17829. After we will calculate the factors of 17823 and 17829 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 17829

Prime factors of 17829 are 3, 7, 283. Prime factorization of 17829 in exponential form is:

17829 = 3² × 7¹ × 283¹

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 17829

List of positive integer factors of 17829 that divides 17823 without a remainder.

1, 3, 7, 9, 21, 63, 283, 849, 1981, 2547, 5943

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17823 and 17829. The biggest common factor number is the GCF number.
So the greatest common factor 17823 and 17829 is 3.

Also check out the Least Common Multiple of 17823 and 17829