Level 6 Puzzle

191 and Level 6

/ ivasallay / Leave a comment
  • 191 is a prime number.
  • Prime factorization: 191 is prime.
  • The exponent of prime number 191 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 191 has exactly 2 factors.
  • Factors of 191: 1, 191
  • Factor pairs: 191 = 1 x 191
  • 191 has no square factors that allow its square root to be simplified. √191 ≈ 13.82027

How do we know that 191 is a prime number? If 191 were not a prime number, then it would be divisible by at least one prime number less than or equal to √191 ≈ 13.8. Since 191 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 191 is a prime number.

There are 22 prime numbers between 100 and 200:

  • The first four of those prime numbers are 101, 103, 107, and 109.
  • The last four of those prime numbers are 191, 193, 197, and 199.

 

2014-30 Level 6

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-07-28

2014-30 Level 6 Logic

2014-30 Level 6 Problems

 

185 and Level 6

/ ivasallay / Leave a comment
185 is a composite number.
Factor pairs: 185 = 1 x 185 or 5 x 37
Factors of 185: 1, 5, 37, 185
Prime factorization: 185 = 5 x 37

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2014-29 Level 6

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-07-21

2014-29 Level 6 Logic

179 and Level 6

/ ivasallay / Leave a comment
  • 179 is a prime number.
  • Prime factorization: 179 is prime.
  • The exponent of prime number 179 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 179 has exactly 2 factors.
  • Factors of 179: 1, 179
  • Factor pairs: 179 = 1 x 179
  • 179 has no square factors that allow its square root to be simplified. √179 ≈ 13.379088

How do we know that 179 is a prime number? If 179 were not a prime number, then it would be divisible by at least one prime number less than or equal to √179 ≈ 13.4. Since 179 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 179 is a prime number.

2014-28 Level 6

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-07-14

2014-28 Level 6 Logic

173 and Level 6

/ ivasallay / Leave a comment
  • 173 is a prime number.
  • Prime factorization: 173 is prime.
  • The exponent of prime number 173 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 173 has exactly 2 factors.
  • Factors of 173: 1, 173
  • Factor pairs: 173 = 1 x 173
  • 173 has no square factors that allow its square root to be simplified. √173 ≈ 13.1529

How do we know that 173 is a prime number? If 173 were not a prime number, then it would be divisible by at least one prime number less than or equal to √173 ≈ 13.2. Since 173 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 173 is a prime number.

2014-27 Level 6

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-07-07

2014-27 Level 6 Logic

166 and Level 6

/ ivasallay / 2 Comments
166 is a composite number.
Factor pairs: 166 = 1 x 166 or 2 x 83
Factors of 166: 1, 2, 83, 166
Prime factorization: 166 = 2 x 83

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2014-26 Level 6

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

2014-26 Level 6 Logic

160 and Level 6

/ ivasallay / Leave a comment
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

154 and Level 6

/ ivasallay / Leave a comment
154 is a composite number.
Factor pairs: 154 = 1 x 154, 2 x 77, 7 x 22, 11 x 14
Factors of 154: 1, 2, 7, 11, 14, 22, 77, 154
Prime factorization: 154 = 2 x 7 x 11

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2014-24 Level 6

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-06-16

2014-24 Level 6 Logic

147 and Level 6

/ ivasallay / 1 Comment

 

147 is a composite number.
Factor pairs:147 = 1 x 147, 3 x 49, or 7 x 21.
Factors of 147: 1, 3, 7, 21, 49, 147.
Prime factorization: 147 = 3 x 7 x 7, which can also be written 147 = 3 x (7^2).

2014-23 Level 6

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-09

2014-23 Level 6 Logic

141 and Level 6

/ ivasallay / 2 Comments

141 is a composite number. Factor pairs: 141 = 1 x 141 or 3 x 47. Factors of 141: 1, 3, 47, 141. Prime factorization: 141 = 3 x 47.

141 is never a clue in the FIND THE FACTORS puzzles.

2014-22 Level 6

Excel file with puzzles and the previous week’s factor solutions: 12 Factors 2014-06-02

2014-22 Level 6 Logic

 

133 and Level 6

/ ivasallay / Leave a comment

133 is a composite number. 133 = 1 x 133 or 7 x 19. Factors of 133: 1, 7, 19, 133. Prime factorization 133 = 7 x 19.

  • The divisibility trick for 7 tells us to split 133 into 13 and 3. We double 3 and find the difference between the double and 13. We get 13 – (2 x 3)  = 13 – 6  = 7 (an obvious multiple of 7) so 7 is a factor of 133.

133 is never a clue in the FIND THE FACTORS puzzles.

2014-21 Level 6

Excel file of puzzles and previous week’s solutions: 10 Factors 2014-05-26

2014-21 Level 6 Logic