What is the Greatest Common Factor of 814 and 825?

Greatest common factor (GCF) of 814 and 825 is 11.

GCF(814,825) = 11

We will now calculate the prime factors of 814 and 825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 814 and 825.

How to find the GCF of 814 and 825?

We will first find the prime factorization of 814 and 825. After we will calculate the factors of 814 and 825 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 825

Prime factors of 825 are 3, 5, 11. Prime factorization of 825 in exponential form is:

825 = 3¹ × 5² × 11¹

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 825

List of positive integer factors of 825 that divides 814 without a remainder.

1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 814 and 825. The biggest common factor number is the GCF number.
So the greatest common factor 814 and 825 is 11.

Also check out the Least Common Multiple of 814 and 825