A Multiplication Based Logic Puzzle

Archive for June, 2014

161 and Level 1

161 is a composite number.
Factor pairs: 161 = 1 x 161 or 7 x 23
Factors of 161: 1, 7, 23, 161
Prime factorization: 161 = 7 x 23

————————————————————————————————————————-

2014-26 Level 1

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-06-30

2014-26 Level 1 Factors

Advertisements

160 and Level 6

160 is a composite number.
Factor pairs: 160 = 1 x 160, 2 x 80, 4 x 40, 5 x 32, 8 x 20, or 10 x 16
Factors of 160: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
Prime factorization: 160 = 2 x 2 x 2 x 2 x 2 x 5, which can also be written 160 = (2^5) x 5

160 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 (the sum of the first eleven prime numbers).

2014-25 Level 6

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23

2014-25 Level 6 Logic

159 and Level 5

159 is a composite number.
Factor pairs: 159 = 1 x 159 or 3 x 53
Factors of 159: 1, 3, 53, 159
Prime factorization: 159 = 3 x 53

————————————————————————————————————————-

2014-25 Level 5

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23

2014-25 Level 5 Logic

158 and Level 4

158 is a composite number.
Factor pairs: 158 = 1 x 158 or 2 x 79
Factors of 158: 1, 2, 79, 158
Prime factorization: 158 = 2 x 79

————————————————————————————————————————-

2014-25 Level 4

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23

2014-25 Level 4 Logic

157 and Level 3

  • 157 is a prime number.
  • Prime factorization: 157 is prime.
  • The exponent of prime number 157 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 157 has exactly 2 factors.
  • Factors of 157: 1, 157
  • Factor pairs: 157 = 1 x 157
  • 157 has no square factors that allow its square root to be simplified. √157 ≈ 12.52996

How do we know that 157 is a prime number? If 157 were not a prime number, then it would be divisible by at least one prime number less than or equal to √157 ≈ 12.5. Since 157 cannot be divided evenly by 2, 3, 5, 7, or 11, we know that 157 is a prime number.

2014-25 Level 3

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23

A Logical Approach to FIND THE FACTORS: Find the column or row with two clues and find their common factor. Write the corresponding factors in the factor column (1st column) and factor row (top row).  Because this is a level three puzzle, you have now written a factor at the top of the factor column. Continue to work from the top of the factor column to the bottom, finding factors and filling in the factor column and the factor row one cell at a time as you go.

2014-25 Level 3 Factors

156 and Level 2

156 is a composite number.
Factor pairs: 156 = 1 x 156, 2 x 78, 3 x 52, 4 x 39, 6 x 26, or 12 x 13
Factors of 156: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
Prime factorization: 156 = 2 x 2 x 3 x 13, which can be written (2^2) x 3 x 13

———————————————————————————————————————

2014-25 Level 2

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23

2014-25 Level 2 Factors

155 and Level 1

155 is a composite number.
Factor pairs: 155 = 1 x 155 or 5 x 31
Factors of 155: 1, 5, 31, 155
Prime factorization: 155 = 5 x 31

———————————————————————————–

 2014-25 Level 1

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23

2014-25 Level 1 Factors

Tag Cloud