What is the Greatest Common Factor of 23829 and 23842?

Greatest common factor (GCF) of 23829 and 23842 is 13.

GCF(23829,23842) = 13

We will now calculate the prime factors of 23829 and 23842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23829 and 23842.

How to find the GCF of 23829 and 23842?

We will first find the prime factorization of 23829 and 23842. After we will calculate the factors of 23829 and 23842 and find the biggest common factor number .

Step-1: Prime Factorization of 23829

Prime factors of 23829 are 3, 13, 47. Prime factorization of 23829 in exponential form is:

23829 = 3¹ × 13² × 47¹

Step-2: Prime Factorization of 23842

Prime factors of 23842 are 2, 7, 13, 131. Prime factorization of 23842 in exponential form is:

23842 = 2¹ × 7¹ × 13¹ × 131¹

Step-3: Factors of 23829

List of positive integer factors of 23829 that divides 23829 without a remainder.

1, 3, 13, 39, 47, 141, 169, 507, 611, 1833, 7943

Step-4: Factors of 23842

List of positive integer factors of 23842 that divides 23829 without a remainder.

1, 2, 7, 13, 14, 26, 91, 131, 182, 262, 917, 1703, 1834, 3406, 11921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23829 and 23842. The biggest common factor number is the GCF number.
So the greatest common factor 23829 and 23842 is 13.

Also check out the Least Common Multiple of 23829 and 23842