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1623 Easter Basket Challenge Puzzle

/ ivasallay / Leave a comment

Today’s Puzzle:

Since I’ve recently made puzzles with a pink, purple, or blue Easter egg as well as some blades of grass blowing in the spring wind, it only makes sense that I would also give you an Easter basket in which to hold those other puzzles.

The puzzle is solved if you have written the numbers 1 to 10 in each of the boldly outlined areas of the puzzle, and if those numbers work with the clues to form four multiplication tables.

Print the puzzles or type the solution in this excel file: 12 Factors 1614-1623.

If you need a little help, here’s the same puzzle with the factor pairs for the clues written in.

And if you want even more help, here’s a 2 1/2 minute video on how to get started. I assume you already know the directions on how to solve this kind of puzzle that I gave at the top of this post.

Factors of 1623:

  • 1623 is a composite number.
  • Prime factorization: 1623 = 3 × 541.
  • 1623 has no exponents greater than 1 in its prime factorization, so √1623 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 1623 has exactly 4 factors.
  • The factors of 1623 are outlined with their factor pair partners in the graphic below.

More About the Number 1623:

1623 is the hypotenuse of a Pythagorean triple:
1023-1260-1623, which is 3 times (341-420-541).

1377 Easter Basket Challenge

/ ivasallay / Leave a comment

Occasionally,  we hear that the number of Easter eggs that are found is one or two less than the number of eggs that were hidden. Still most of the time, all the eggs and candies do get found. You really have no trouble finding all those goodies, and the Easter Egg Hunt seems like it is over in seconds.  You can find Easter Eggs but can you find factors? Here’s an Easter Basket Find the Factors 1 – 10 Challenge Puzzle for you. I guarantee it won’t be done in seconds. Can you find all the factors? I dare you to try!

Print the puzzles or type the solution in this excel file: 10 Factors 1373-1388

Now I’ll mention a few facts about the number 1377:

  • 1377 is a composite number.
  • Prime factorization: 1377 = 3 × 3 × 3 × 3 × 17, which can be written 1377 = 3⁴ × 17
  • 1377 has at least one exponent greater than 1 in its prime factorization so √1377 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1377 = (√81)(√17) = 9√17
  • The exponents in the prime factorization are 4 and 1. Adding one to each exponent and multiplying we get (4 + 1)(1 + 1) = 5 × 2 = 10. Therefore 1377 has exactly 10 factors.
  • The factors of 1377 are outlined with their factor pair partners in the graphic below.

1377 is the sum of two squares:
36² + 9² = 1377

1377 is the hypotenuse of a Pythagorean triple:
648-1215-1377 which is (8-15-17) times 81
and can also be calculated from 2(36)(9), 36² – 9², 36² + 9²