What is the Greatest Common Factor of 33408 and 33414?

Greatest common factor (GCF) of 33408 and 33414 is 6.

GCF(33408,33414) = 6

We will now calculate the prime factors of 33408 and 33414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33408 and 33414.

How to find the GCF of 33408 and 33414?

We will first find the prime factorization of 33408 and 33414. After we will calculate the factors of 33408 and 33414 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 33414

Prime factors of 33414 are 2, 3, 5569. Prime factorization of 33414 in exponential form is:

33414 = 2¹ × 3¹ × 5569¹

Step-3: Factors of 33408

List of positive integer factors of 33408 that divides 33408 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

Step-4: Factors of 33414

List of positive integer factors of 33414 that divides 33408 without a remainder.

1, 2, 3, 6, 5569, 11138, 16707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33408 and 33414. The biggest common factor number is the GCF number.
So the greatest common factor 33408 and 33414 is 6.

Also check out the Least Common Multiple of 33408 and 33414