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Today’s Puzzle:
Write the numbers from 1 to 12 in both the first column and the top row so that the given clues are the products of the numbers you write.
Factors of 1731:
- 1731 is a composite number.
- Prime factorization: 1731 = 3 × 577.
- 1731 has no exponents greater than 1 in its prime factorization, so √1731 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 1731 has exactly 4 factors.
- The factors of 1731 are outlined with their factor pair partners in the graphic below.
More About the Number 1731:
1731 is the hypotenuse of a Pythagorean triple:
144-1725-1731 which is 3 times (48-575-577).
OEIS.org informs us that 1731 is the sum of the squares of three consecutive prime numbers. Let’s find those three prime numbers. Since √(1731/3) rounds to 24, I’m guessing the middle prime number is 23. The prime numbers occurring before and after it are 19 and 29.
Is 19² + 23² + 29² = 1731? Yes, it is!
Here are some other ways that 1731 is the sum of three squares:
41² + 7² + 1² = 1731,
41² + 5² + 5² = 1731,
37² + 19² + 1² = 1731, and
29² + 29² + 7² = 1731.