What is the Greatest Common Factor of 17404 and 17408?

Greatest common factor (GCF) of 17404 and 17408 is 4.

GCF(17404,17408) = 4

We will now calculate the prime factors of 17404 and 17408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17404 and 17408.

How to find the GCF of 17404 and 17408?

We will first find the prime factorization of 17404 and 17408. After we will calculate the factors of 17404 and 17408 and find the biggest common factor number .

Step-1: Prime Factorization of 17404

Prime factors of 17404 are 2, 19, 229. Prime factorization of 17404 in exponential form is:

17404 = 2² × 19¹ × 229¹

Step-2: Prime Factorization of 17408

Prime factors of 17408 are 2, 17. Prime factorization of 17408 in exponential form is:

17408 = 2¹⁰ × 17¹

Step-3: Factors of 17404

List of positive integer factors of 17404 that divides 17404 without a remainder.

1, 2, 4, 19, 38, 76, 229, 458, 916, 4351, 8702

Step-4: Factors of 17408

List of positive integer factors of 17408 that divides 17404 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 256, 272, 512, 544, 1024, 1088, 2176, 4352, 8704

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17404 and 17408. The biggest common factor number is the GCF number.
So the greatest common factor 17404 and 17408 is 4.

Also check out the Least Common Multiple of 17404 and 17408