What is the Greatest Common Factor of 33400 and 33408?

Greatest common factor (GCF) of 33400 and 33408 is 8.

GCF(33400,33408) = 8

We will now calculate the prime factors of 33400 and 33408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33400 and 33408.

How to find the GCF of 33400 and 33408?

We will first find the prime factorization of 33400 and 33408. After we will calculate the factors of 33400 and 33408 and find the biggest common factor number .

Step-1: Prime Factorization of 33400

Prime factors of 33400 are 2, 5, 167. Prime factorization of 33400 in exponential form is:

33400 = 2³ × 5² × 167¹

Step-2: Prime Factorization of 33408

Prime factors of 33408 are 2, 3, 29. Prime factorization of 33408 in exponential form is:

33408 = 2⁷ × 3² × 29¹

Step-3: Factors of 33400

List of positive integer factors of 33400 that divides 33400 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 167, 200, 334, 668, 835, 1336, 1670, 3340, 4175, 6680, 8350, 16700

Step-4: Factors of 33408

List of positive integer factors of 33408 that divides 33400 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 29, 32, 36, 48, 58, 64, 72, 87, 96, 116, 128, 144, 174, 192, 232, 261, 288, 348, 384, 464, 522, 576, 696, 928, 1044, 1152, 1392, 1856, 2088, 2784, 3712, 4176, 5568, 8352, 11136, 16704

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33400 and 33408. The biggest common factor number is the GCF number.
So the greatest common factor 33400 and 33408 is 8.

Also check out the Least Common Multiple of 33400 and 33408