321 I Heard the Bells on Christmas Day

321 is made solely from three consecutive numbers so it can be evenly divided by 3.

  • 321 is a composite number.
  • Prime factorization: 321 = 3 x 107
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 321 has exactly 4 factors.
  • Factors of 321: 1, 3, 107, 321
  • Factor pairs: 321 = 1 x 321 or 3 x 107
  • 321 has no square factors that allow its square root to be simplified. √321 ≈ 17.916
I heard the bells
Print the puzzles or type the factors on this excel file: 10 Factors 2014-12-08
  1. I heard the bells on Christmas day
    Their old familiar carols play,
    And wild and sweet the words repeat
    Of peace on earth, good will to men.
  2. I thought how, as the day had come,
    The belfries of all Christendom
    Had rolled along th’unbroken song
    Of peace on earth, good will to men.
  3. And in despair I bowed my head:
    “There is no peace on earth,” I said,
    “For hate is strong and mocks the song
    Of peace on earth, good will to men.”
  4. Then pealed the bells more loud and deep:
    “God is not dead, nor doth he sleep;
    The wrong shall fail, the right prevail,
    With peace on earth, good will to men.”
  5. Till, ringing, singing, on its way,
    The world revolved from night to day,
    A voice, a chime, a chant sublime,
    Of peace on earth, good will to men!
Text: Henry Wadsworth Longfellow, 1807-1882
I heard the bells factors

2 thoughts on “321 I Heard the Bells on Christmas Day

  1. Okay, I hear my husband coming in from clearing the snow, but I managed to do my first find-the-factor puzzle. I started with a level two, the one with number 319, flew through that and a the level four on this page, then was humbled by the level five, Finished it in time to be signing off. Spoiler alert…the top row is 5 2 1 10 6 4 9 8 3 7 right? Fun!

    • Yes.
      I design the puzzles to have only one solution so you can be sure that if the factors you find work, then you have found the correct solution. About a week after I publish the puzzles, I update the posts with either the correct factors or a table showing a way to arrive at the correct solution logically.

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