1691 Jack 0’Lantern Time

Today’s Puzzle:

This smiling Jack O’Lantern actually has a few tricks up his sleeve. Don’t let yourself get fooled by any of them. Using logic, write the numbers from 1 to 12 in the first column as well as in the top row so that those numbers and the given clues can be a multiplication table.

Have a safe and happy Halloween!

Here’s the same puzzle with just the clues:

Factors of 1691:

  • 1691 is a composite number.
  • Prime factorization: 1691 = 19 × 89.
  • 1691 has no exponents greater than 1 in its prime factorization, so √1691 cannot be simplified.
  • The exponents in the prime factorization are 1 and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1691 has exactly 4 factors.
  • The factors of 1691 are outlined with their factor pair partners in the graphic below.

More About the Number 1691:

1691 is the hypotenuse of a Pythagorean triple:
741-1520-1691, which is 19 times (39-80-89).

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