What is the Greatest Common Factor of 31822 and 31829?

Greatest common factor (GCF) of 31822 and 31829 is 7.

GCF(31822,31829) = 7

We will now calculate the prime factors of 31822 and 31829, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31822 and 31829.

How to find the GCF of 31822 and 31829?

We will first find the prime factorization of 31822 and 31829. After we will calculate the factors of 31822 and 31829 and find the biggest common factor number .

Step-1: Prime Factorization of 31822

Prime factors of 31822 are 2, 7, 2273. Prime factorization of 31822 in exponential form is:

31822 = 2¹ × 7¹ × 2273¹

Step-2: Prime Factorization of 31829

Prime factors of 31829 are 7, 4547. Prime factorization of 31829 in exponential form is:

31829 = 7¹ × 4547¹

Step-3: Factors of 31822

List of positive integer factors of 31822 that divides 31822 without a remainder.

1, 2, 7, 14, 2273, 4546, 15911

Step-4: Factors of 31829

List of positive integer factors of 31829 that divides 31822 without a remainder.

1, 7, 4547

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31822 and 31829. The biggest common factor number is the GCF number.
So the greatest common factor 31822 and 31829 is 7.

Also check out the Least Common Multiple of 31822 and 31829