What is the Greatest Common Factor of 814 and 821?

Greatest common factor (GCF) of 814 and 821 is 1.

GCF(814,821) = 1

We will now calculate the prime factors of 814 and 821, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 814 and 821.

How to find the GCF of 814 and 821?

We will first find the prime factorization of 814 and 821. After we will calculate the factors of 814 and 821 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 821

Prime factors of 821 are 821. Prime factorization of 821 in exponential form is:

821 = 821¹

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 821

List of positive integer factors of 821 that divides 814 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 814 and 821. The biggest common factor number is the GCF number.
So the greatest common factor 814 and 821 is 1.

Also check out the Least Common Multiple of 814 and 821