What is the Greatest Common Factor of 17408 and 17425?

Greatest common factor (GCF) of 17408 and 17425 is 17.

GCF(17408,17425) = 17

We will now calculate the prime factors of 17408 and 17425, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17408 and 17425.

How to find the GCF of 17408 and 17425?

We will first find the prime factorization of 17408 and 17425. After we will calculate the factors of 17408 and 17425 and find the biggest common factor number .

Step-1: Prime Factorization of 17408

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

17408 = 2¹⁰ × 17¹

Step-2: Prime Factorization of 17425

Prime factors of 17425 are 5, 17, 41. Prime factorization of 17425 in exponential form is:

17425 = 5² × 17¹ × 41¹

Step-3: Factors of 17408

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

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

Step-4: Factors of 17425

List of positive integer factors of 17425 that divides 17408 without a remainder.

1, 5, 17, 25, 41, 85, 205, 425, 697, 1025, 3485

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17408 and 17425. The biggest common factor number is the GCF number.
So the greatest common factor 17408 and 17425 is 17.

Also check out the Least Common Multiple of 17408 and 17425