What is the Greatest Common Factor of 17408 and 17416?

Greatest common factor (GCF) of 17408 and 17416 is 8.

GCF(17408,17416) = 8

We will now calculate the prime factors of 17408 and 17416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17408 and 17416.

How to find the GCF of 17408 and 17416?

We will first find the prime factorization of 17408 and 17416. After we will calculate the factors of 17408 and 17416 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 17416

Prime factors of 17416 are 2, 7, 311. Prime factorization of 17416 in exponential form is:

17416 = 2³ × 7¹ × 311¹

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 17416

List of positive integer factors of 17416 that divides 17408 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 311, 622, 1244, 2177, 2488, 4354, 8708

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17408 and 17416. The biggest common factor number is the GCF number.
So the greatest common factor 17408 and 17416 is 8.

Also check out the Least Common Multiple of 17408 and 17416