A Multiplication Based Logic Puzzle

Posts tagged ‘tree’

702 A Couple of Christmas Factor Trees

Since the sum of its digits equals nine, 702 is divisible by nine.

702 is the product of consecutive integers: 26 x 27 = 702. Numbers that can be expressed as such products are known as Pronic numbers.

It seems only natural to make factor trees based on those two multiplication facts:

702 Factor Trees

Here’s more facts about the number 702: It is the sum of consecutive prime numbers 349 and 353.

It is also the sum of the seventeen prime numbers from 7 to 73.

And because 13 is one of its factors, 702 is the hypotenuse of Pythagorean triple 270-648-702. Notice that the short leg is a permutation of 702.

Today’s Find the Factors puzzle looks like a couple of small Christmas trees.

702 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2015-11-30

—————————————————————————————————

  • 702 is a composite number.
  • Prime factorization: 702 = 2 x 3 x 3 x 3 x 13, which can be written 702 = 2 x (3^3) x 13
  • The exponents in the prime factorization are 1, 3, and 1. Adding one to each and multiplying we get (1 + 1)(3 + 1)(1 + 1) = 2 x 4 x 2 = 16. Therefore 702 has exactly 16 factors.
  • Factors of 702: 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702
  • Factor pairs: 702 = 1 x 702, 2 x 351, 3 x 234, 6 x 117, 9 x 78, 13 x 54, 18 x 39, or 26 x 27
  • Taking the factor pair with the largest square number factor, we get √702 = (√9)(√78) = 3√78 ≈ 26.49528.

—————————————————————————————————

702 Logic

14 Oh Christmas Tree

14 is a composite number. 14 = 1 x 14 or 2 x 7. Factors of 14: 1, 2, 7, 14. Prime factorization: 14 = 2 x 7.

When 14 is a clue in the FIND THE FACTORS  1 – 10 or 1 – 12 puzzles, use 2 and 7 as the factors.

O Christmas Tree, O Christmas Tree,

How lovely are your branches…

Do Christmas factor trees have lovely branches?  It depends on how they are constructed. For example here are 2 of the many possible factor trees for 1680. I think one of them is more lovely than the other.

1680.21680.1

This blog is actually about a logic puzzle that is based on the multiplication table. Today we have puzzles that look like Christmas trees, garland, lights, or blocks and a bright star for the very top.

Directions to solve the puzzles: In both the top row and the first column place the numbers 1 – 10 so that they are factors of the given clues. It may be more challenging than you think, especially for the higher level puzzles. If you click 10 Factors 2013-12-09, you can print the puzzles in color or black and white from an excel spreadsheet or you can type the answers directly on the spreadsheet. You must have a spreadsheet program on your device to access the file.

2013-12-09.12013-12-09.2

2013-12-09.32013-12-09.4

2013-12-09.52013-12-09.6

Tag Cloud