What is the Greatest Common Factor of 17408 and 17424?

Greatest common factor (GCF) of 17408 and 17424 is 16.

GCF(17408,17424) = 16

We will now calculate the prime factors of 17408 and 17424, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17408 and 17424.

How to find the GCF of 17408 and 17424?

We will first find the prime factorization of 17408 and 17424. After we will calculate the factors of 17408 and 17424 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 17424

Prime factors of 17424 are 2, 3, 11. Prime factorization of 17424 in exponential form is:

17424 = 2⁴ × 3² × 11²

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 17424

List of positive integer factors of 17424 that divides 17408 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 66, 72, 88, 99, 121, 132, 144, 176, 198, 242, 264, 363, 396, 484, 528, 726, 792, 968, 1089, 1452, 1584, 1936, 2178, 2904, 4356, 5808, 8712

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17408 and 17424. The biggest common factor number is the GCF number.
So the greatest common factor 17408 and 17424 is 16.

Also check out the Least Common Multiple of 17408 and 17424