# 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 ——————————————————————————————————————- 