A Multiplication Based Logic Puzzle

  • 43 is a prime number.
  • Prime factorization: 43 is prime.
  • The exponent of prime number 43 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 43 has exactly 2 factors.
  • Factors of 43: 1, 43
  • Factor pairs: 43 = 1 x 43
  • 43 has no square factors that allow its square root to be simplified. √43 ≈ 6.5574

How do we know that 43 is a prime number? If 43 were not a prime number, then it would be divisible by at least one prime number less than or equal to √43 ≈ 6.6. Since 43 cannot be divided evenly by 2, 3, or 5, we know that 43 is a prime number.

43 is never a clue in the FIND THE FACTORS puzzles.

So far today FIND THE FACTORS has received nearly four times as many views as its previous high. When I investigated why, I discovered one of the reasons was a blog called mathematicsgames.wordpress.com. On that blog was this post recommending the FIND THE FACTORS puzzles. I am excited for the great write-up and the new people who have looked at the puzzles and used the excel file I made! I am humbled that mathematicsgames wrote this post, and I’m also quite proud to reblog it here.

Mathematics - Games

For a puzzle with a difference which requires both logic and multiplication try a Find the Factors puzzle from Iva Sallay on her Find the Factors blog. In this Find the Factors 1-10 puzzle can you place the numbers 1 to 10 in the first row and the first column to make the multiplication table work? Iva Sallay has clearly explained the puzzles here: How to Find the Factors.

New puzzles are published each week, I like the Excel files provided with puzzles of varying levels of difficulty. You will also find many hints and tips in the various posts. See Hooked on Factoring for example, a post giving techniques for solving the puzzles and an Excel file of puzzles.

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