What is the Greatest Common Factor of 814 and 828?

Greatest common factor (GCF) of 814 and 828 is 2.

GCF(814,828) = 2

We will now calculate the prime factors of 814 and 828, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 814 and 828.

How to find the GCF of 814 and 828?

We will first find the prime factorization of 814 and 828. After we will calculate the factors of 814 and 828 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 828

Prime factors of 828 are 2, 3, 23. Prime factorization of 828 in exponential form is:

828 = 2² × 3² × 23¹

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 828

List of positive integer factors of 828 that divides 814 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 814 and 828. The biggest common factor number is the GCF number.
So the greatest common factor 814 and 828 is 2.

Also check out the Least Common Multiple of 814 and 828