Today might not be the 312th day of the year, but here’s a fun fact about the number 312:

The 312th day of the year; 312 = 0!*5! + 1!*4! + 2!*3! + 3!*2! + 4!*1! + 5!*0! https://t.co/3p8O4ZS5En

— On This Day in Math (@OnThisDayinMath) November 8, 2015

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• 312 is a composite number.
• Prime factorization: 312 = 2 x 2 x 2 x 3 x 13, which can be written 312 = (2^3) x 3 x 13
• The exponents in the prime factorization are 3, 1, and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1)(1 + 1) = 4 x 2 x 2 = 16. Therefore 312 has exactly 16 factors.
• Factors of 312: 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
• Factor pairs: 312 = 1 x 312, 2 x 156, 3 x 104, 4 x 78, 6 x 52, 8 x 39, 12 x 26, or 13 x 24
• Taking the factor pair with the largest square number factor, we get √312 = (√4)(√78) = 2√78 ≈ 17.664

The night of December 5th, Mikulás, or St. Nickolas, will visit homes in Hungary, some neighboring countries, and even a few houses in the United States.  Children who have been good will awaken to find their shoes filled with little treats such as candy, fruit or nuts. Since all children are occasionally a little bit naughty, they will also find virgács, a small collection of twigs that have been spray-painted gold and decoratively bound together.  Virgács are not sold in the United States, so St Nickolas will be making some himself using the bristles from a natural broom.  The finished product should look like today’s puzzle.