#math trivia #168 solution

The number of positive divisors of 168 is 16. Given the factorization of 168, we know that any positive divisor must have the form

2i * 3j * 7k

where i is between 0 and 3, j is 0 or 1, and k is 0 or 1. All together, there are 4*2*2 = 16 possible combinations of i, j and k. (No two combinations produce the same divisor, or otherwise a divisor would have two different prime factorizations, which is not possible according to the Unique Factorization Theorem.)

The 16 divisors and their corresponding factorizations are listed in the following table for reference.

Divisor Factorization
1 20 * 30 * 70
2 21 * 30 * 70
3 20 * 31 * 70
4 22 * 30 * 70
6 20 * 31 * 70
7 20 * 30 * 71
8 23 * 30 * 70
12 22 * 31 * 70
14 21 * 30 * 71
21 20 * 31 * 71
24 23 * 31 * 70
28 22 * 30 * 71
42 22 * 31 * 71
56 23 * 30 * 71
84 22 * 31 * 71
168 23 * 31 * 71

One thought on “#math trivia #168 solution

  1. Pingback: #math trivia #240 solution | modulomathy.com

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