What is the Greatest Common Factor of 814 and 824?

Greatest common factor (GCF) of 814 and 824 is 2.

GCF(814,824) = 2

We will now calculate the prime factors of 814 and 824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 814 and 824.

How to find the GCF of 814 and 824?

We will first find the prime factorization of 814 and 824. After we will calculate the factors of 814 and 824 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 824

Prime factors of 824 are 2, 103. Prime factorization of 824 in exponential form is:

824 = 2³ × 103¹

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 824

List of positive integer factors of 824 that divides 814 without a remainder.

1, 2, 4, 8, 103, 206, 412

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 814 and 824. The biggest common factor number is the GCF number.
So the greatest common factor 814 and 824 is 2.

Also check out the Least Common Multiple of 814 and 824