1604 and a Big Level One

Today’s Puzzle:

1604 was my house number most of my childhood. Perhaps this number is making me feel a little more playful. I decided my next few puzzles would be based on a 1 to 14 multiplication table. I find that I personally use clues like 26, 39, 52, 65, 78, 104, 143, and 169 often in life. For example, why are there 52 playing cards in a deck of cards? To help you get more familiar with the 1 to14 multiplication table, we will start with this level one puzzle:

Print the puzzles or type the solution in this excel file: 14 Factors 1604-1612.

Factors of 1604:

  • 1604 is a composite number.
  • Prime factorization: 1604 = 2 × 2 × 401, which can be written 1604 = 2² × 401
  • 1604 has at least one exponent greater than 1 in its prime factorization so √1604 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1604 = (√4)(√401) = 2√401
  • The exponents in the prime factorization are 2 and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1) = 3 × 2 = 6. Therefore 1604 has exactly 6 factors.
  • The factors of 1604 are outlined with their factor pair partners in the graphic below.

More about the Number 1604:

1604 is the sum of two squares:
40² + 2² = 1604.

1604 is the hypotenuse of a Pythagorean triple:
160-1596-1604, calculated from 2(40)(2), 40² – 2², 40² + 2².
It is also 4 times (40-399-401).

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