What is the Greatest Common Factor of 33814 and 33825?

Greatest common factor (GCF) of 33814 and 33825 is 11.

GCF(33814,33825) = 11

We will now calculate the prime factors of 33814 and 33825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33814 and 33825.

How to find the GCF of 33814 and 33825?

We will first find the prime factorization of 33814 and 33825. After we will calculate the factors of 33814 and 33825 and find the biggest common factor number .

Step-1: Prime Factorization of 33814

Prime factors of 33814 are 2, 11, 29, 53. Prime factorization of 33814 in exponential form is:

33814 = 2¹ × 11¹ × 29¹ × 53¹

Step-2: Prime Factorization of 33825

Prime factors of 33825 are 3, 5, 11, 41. Prime factorization of 33825 in exponential form is:

33825 = 3¹ × 5² × 11¹ × 41¹

Step-3: Factors of 33814

List of positive integer factors of 33814 that divides 33814 without a remainder.

1, 2, 11, 22, 29, 53, 58, 106, 319, 583, 638, 1166, 1537, 3074, 16907

Step-4: Factors of 33825

List of positive integer factors of 33825 that divides 33814 without a remainder.

1, 3, 5, 11, 15, 25, 33, 41, 55, 75, 123, 165, 205, 275, 451, 615, 825, 1025, 1353, 2255, 3075, 6765, 11275

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33814 and 33825. The biggest common factor number is the GCF number.
So the greatest common factor 33814 and 33825 is 11.

Also check out the Least Common Multiple of 33814 and 33825