1316 Hard Candy

 

When I have a cold or a cough, I often have a piece of hard candy in my mouth. These red cinnamon candies are tasty, but they aren’t very good for soothing throats! Will this red hot cinnamon candy puzzle be too hard for you to solve? It may be a little bit of a challenge, but I’m sure you can solve it if you let logic be your guide the entire time. 

Print the puzzles or type the solution in this excel file: 12 factors 1311-1319

Now I’ll share some information about the number 1316:

  • 1316 is a composite number.
  • Prime factorization: 1316 = 2 × 2 × 7 × 47, which can be written 1316 = 2² × 7 × 47
  • The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1316 has exactly 12 factors.
  • Factors of 1316: 1, 2, 4, 7, 14, 28, 47, 94, 188, 329, 658, 1316
  • Factor pairs: 1316 = 1 × 1316, 2 × 658, 4 × 329, 7 × 188, 14 × 94, or 28 × 47
  • Taking the factor pair with the largest square number factor, we get √1316 = (√4)(√329) = 2√329 ≈ 36.27671

1316 is the difference of two squares two different ways:
330² – 328² = 1316
54² – 40² = 1316 

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