What is the Greatest Common Factor of 10822 and 10829?

Greatest common factor (GCF) of 10822 and 10829 is 7.

GCF(10822,10829) = 7

We will now calculate the prime factors of 10822 and 10829, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10822 and 10829.

How to find the GCF of 10822 and 10829?

We will first find the prime factorization of 10822 and 10829. After we will calculate the factors of 10822 and 10829 and find the biggest common factor number .

Step-1: Prime Factorization of 10822

Prime factors of 10822 are 2, 7, 773. Prime factorization of 10822 in exponential form is:

10822 = 2¹ × 7¹ × 773¹

Step-2: 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-3: Factors of 10822

List of positive integer factors of 10822 that divides 10822 without a remainder.

1, 2, 7, 14, 773, 1546, 5411

Step-4: Factors of 10829

List of positive integer factors of 10829 that divides 10822 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10822 and 10829. The biggest common factor number is the GCF number.
So the greatest common factor 10822 and 10829 is 7.

Also check out the Least Common Multiple of 10822 and 10829