Today’s Puzzle:

There are several clues in this puzzle with more than one factor pair, but if you use logic every step of the way, you can still write the factors 1 to 12 in the appropriate places to turn the puzzle into a multiplication table.

Factors of 1642:

• 1642 is a composite number.
• Prime factorization: 1642 = 2 × 821.
• 1642 has no exponents greater than 1 in its prime factorization, so √1642 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 1642 has exactly 4 factors.
• The factors of 1642 are outlined with their factor pair partners in the graphic below.

More About the Number 1642:

1642 is the sum of two squares:
39² + 11² = 1642.

1642 is the hypotenuse of a Pythagorean triple:
858-1400-1642, calculated from 2(39)(11), 39² – 11², 39² + 11².
That triple is also 2 times (429-700-821).