What is the Greatest Common Factor of 33808 and 33814?

Greatest common factor (GCF) of 33808 and 33814 is 2.

GCF(33808,33814) = 2

We will now calculate the prime factors of 33808 and 33814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33808 and 33814.

How to find the GCF of 33808 and 33814?

We will first find the prime factorization of 33808 and 33814. After we will calculate the factors of 33808 and 33814 and find the biggest common factor number .

Step-1: Prime Factorization of 33808

Prime factors of 33808 are 2, 2113. Prime factorization of 33808 in exponential form is:

33808 = 2⁴ × 2113¹

Step-2: 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-3: Factors of 33808

List of positive integer factors of 33808 that divides 33808 without a remainder.

1, 2, 4, 8, 16, 2113, 4226, 8452, 16904

Step-4: Factors of 33814

List of positive integer factors of 33814 that divides 33808 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33808 and 33814. The biggest common factor number is the GCF number.
So the greatest common factor 33808 and 33814 is 2.

Also check out the Least Common Multiple of 33808 and 33814