What is the Greatest Common Factor of 10829 and 10842?

Greatest common factor (GCF) of 10829 and 10842 is 13.

GCF(10829,10842) = 13

We will now calculate the prime factors of 10829 and 10842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10829 and 10842.

How to find the GCF of 10829 and 10842?

We will first find the prime factorization of 10829 and 10842. After we will calculate the factors of 10829 and 10842 and find the biggest common factor number .

Step-1: Prime Factorization of 10829

Prime factors of 10829 are 7, 13, 17. Prime factorization of 10829 in exponential form is:

10829 = 7² × 13¹ × 17¹

Step-2: Prime Factorization of 10842

Prime factors of 10842 are 2, 3, 13, 139. Prime factorization of 10842 in exponential form is:

10842 = 2¹ × 3¹ × 13¹ × 139¹

Step-3: Factors of 10829

List of positive integer factors of 10829 that divides 10829 without a remainder.

1, 7, 13, 17, 49, 91, 119, 221, 637, 833, 1547

Step-4: Factors of 10842

List of positive integer factors of 10842 that divides 10829 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 139, 278, 417, 834, 1807, 3614, 5421

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10829 and 10842. The biggest common factor number is the GCF number.
So the greatest common factor 10829 and 10842 is 13.

Also check out the Least Common Multiple of 10829 and 10842