What is the Greatest Common Factor of 803 and 814?

Greatest common factor (GCF) of 803 and 814 is 11.

GCF(803,814) = 11

We will now calculate the prime factors of 803 and 814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 803 and 814.

How to find the GCF of 803 and 814?

We will first find the prime factorization of 803 and 814. After we will calculate the factors of 803 and 814 and find the biggest common factor number .

Step-1: Prime Factorization of 803

Prime factors of 803 are 11, 73. Prime factorization of 803 in exponential form is:

803 = 11¹ × 73¹

Step-2: 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-3: Factors of 803

List of positive integer factors of 803 that divides 803 without a remainder.

1, 11, 73

Step-4: Factors of 814

List of positive integer factors of 814 that divides 803 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 803 and 814. The biggest common factor number is the GCF number.
So the greatest common factor 803 and 814 is 11.

Also check out the Least Common Multiple of 803 and 814