1401 Roasting Over an Open Fire

I went camping last week. My family roasted hotdogs. Some people refer to them as mystery meat. Others roasted marshmallows. I was surprised to learn that almost all brands of marshmallows have blue dye in them.  I’m told that without that blue dye the marshmallows will lose their whiteness as they sit on store shelves. Why they have to be that white is a mystery to me.

Here’s a mystery level puzzle for you to solve. It looks a lot like the utensil that was used to roast the hotdogs and marshmallows.

Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Now I’ll tell you something about the number 1401:

  • 1401 is a composite number.
  • Prime factorization: 1401 = 3 × 467
  • 1401 has no exponents greater than 1 in its prime factorization, so √1401 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 1401 has exactly 4 factors.
  • The factors of 1401 are outlined with their factor pair partners in the graphic below.

1401 is the difference of two squares in two different ways. Can you figure out what those ways are?