### 455 and Level 6

I don’t mean to sound greedy, but if there were 13 days of Christmas instead of only 12, my true love would give me **455** gifts instead of only 364. That’s because the sum of the first 13 triangular numbers is **455**. Come on, that’s 91 more gifts. Funny thing, 91 is one of the factors of **455**. Also, I know I’m not the first person to notice that (13 x 14 x 15)/6 = **455**. As I’m sure you can see, **455** is a fabulous tetrahedral number.

Print the puzzles or type the factors on this excel file: 12 Factors 2015-04-06

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- 455 is a composite number.
- Prime factorization: 455 = 5 x 7 x 13
- The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8. Therefore 445 has exactly 8 factors.
- Factors of 455: 1, 5, 7, 13, 35, 65, 91, 455
- Factor pairs: 455 = 1 x 455, 5 x 91, 7 x 65, or 13 x 35
- 455 has no square factors that allow its square root to be simplified. √455 ≈ 21.3307

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