1573 Ring Out Wild Bells

Today’s Puzzle:

Here are the first two verses of Alfred Lord Tennyson’s Ring Out Wild Bells:

Ring out, wild bells, to the wild sky,
The flying cloud, the frosty light;
The year is dying in the night;
Ring out, wild bells, and let him die.

Ring out the old, ring in the new,
Ring, happy bells, across the snow:
The year is going, let him go;
Ring out the false, ring in the true.

I think we are all ready for 2020 to “die” so we can ring in 2021. You can get started with this bell-shaped puzzle. Use logic to find its unique solution.

Print the puzzles or type the solution in this excel file: 12 Factors 1558-1573

Factors of 1573:

This is my 1573rd post, so let’s find the factors of 1573.

  • 1573 is a composite number.
  • Prime factorization: 1573 = 11 × 11 × 13, which can be written 1573 = 11² × 13
  • 1573 has at least one exponent greater than 1 in its prime factorization so √1573 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1573 = (√121)(√13) = 11√13
  • 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 1573 has exactly 6 factors.
  • The factors of 1573 are outlined with their factor pair partners in the graphic below.

More about the number 1573:

1573 is the sum of two squares:
33² + 22² = 1573.

1573 is the hypotenuse of a Pythagorean triple:
605-1452-1573, calculated from 33² – 22², 2(33)(22), 33² + 22².
It is also (5-12-13) times 121.