What is the Greatest Common Factor of 825 and 838?

Greatest common factor (GCF) of 825 and 838 is 1.

GCF(825,838) = 1

We will now calculate the prime factors of 825 and 838, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 825 and 838.

How to find the GCF of 825 and 838?

We will first find the prime factorization of 825 and 838. After we will calculate the factors of 825 and 838 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 838

Prime factors of 838 are 2, 419. Prime factorization of 838 in exponential form is:

838 = 2¹ × 419¹

Step-3: Factors of 825

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

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

Step-4: Factors of 838

List of positive integer factors of 838 that divides 825 without a remainder.

1, 2, 419

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 825 and 838. The biggest common factor number is the GCF number.
So the greatest common factor 825 and 838 is 1.

Also check out the Least Common Multiple of 825 and 838