grave markers

1526 Grave Marker

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Today’s Puzzle:

It’s almost Halloween! This is my favorite kind of grave marker, one that is really just a Find the Factors puzzle in disguise. It’s only a level one, so it isn’t very tricky. I hope you find it a real treat!

Here’s the same puzzle but requiring less ink to print:

 

Neighbors have decorated part of their yard to look like a mini graveyard for Halloween. I think my grave marker would fit right in!

Factors of 1526:

  • 1526 is a composite number.
  • Prime factorization: 1526 = 2 × 7 × 109.
  • 1526 has no exponents greater than 1 in its prime factorization, so √1526 cannot be simplified.
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1526 has exactly 8 factors.
  • The factors of 1526 are outlined with their factor pair partners in the graphic below.

Another Fact about the Number 1526:

1526 is the hypotenuse of a Pythagorean triple:
840-1274-1526 which is 14 times (60-91-109)

923 Grave Marker

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To me, graveyards are beautiful places where the dearly departed are laid to rest. Find A Grave and Billiongraves are two genealogical sources that assist individuals in finding gravesites. When my son and I visited graveyards in Hungary and Slovakia a few years ago, we saw many wood and stone grave markers that had been eroded by weather. Some were almost impossible to read. We also suspect some people were too poor when they died to get a headstone of any type. We were very excited when we saw any readable grave markers with our family surnames.

Recently on twitter, I saw these paintings of gothic graveyards by M J Forster. I knew immediately I wanted to include them in this post. The paintings are quite stunning.

Finding departed ancestors can sometimes be difficult, but very rewarding. Finding the factors in today’s puzzle will be very easy:

Print the puzzles or type the solution on this excel file: 12 factors 923-931

Here’s a fun fact about the number 923:

OEIS.org informs us that 923(923 + 1) = 852,852. Below are two of the MANY possible factor trees for 852,852. The first one includes factor trees for 923 and 924, the second one shows why their product uses digits that repeat itself in order.

  • 923 is a composite number.
  • Prime factorization: 923 = 13 × 71
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 923 has exactly 4 factors.
  • Factors of 923: 1, 13, 71, 923
  • Factor pairs: 923 = 1 × 923 or 13 × 71
  • 923 has no square factors that allow its square root to be simplified. √923 ≈ 30.380915