What is the Greatest Common Factor of 814 and 822?

Greatest common factor (GCF) of 814 and 822 is 2.

GCF(814,822) = 2

We will now calculate the prime factors of 814 and 822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 814 and 822.

How to find the GCF of 814 and 822?

We will first find the prime factorization of 814 and 822. After we will calculate the factors of 814 and 822 and find the biggest common factor number .

Step-1: Prime Factorization of 814

Prime factors of 814 are 2, 11, 37. Prime factorization of 814 in exponential form is:

814 = 2¹ × 11¹ × 37¹

Step-2: Prime Factorization of 822

Prime factors of 822 are 2, 3, 137. Prime factorization of 822 in exponential form is:

822 = 2¹ × 3¹ × 137¹

Step-3: Factors of 814

List of positive integer factors of 814 that divides 814 without a remainder.

1, 2, 11, 22, 37, 74, 407

Step-4: Factors of 822

List of positive integer factors of 822 that divides 814 without a remainder.

1, 2, 3, 6, 137, 274, 411

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 814 and 822. The biggest common factor number is the GCF number.
So the greatest common factor 814 and 822 is 2.

Also check out the Least Common Multiple of 814 and 822