number puzzle

203 and Level 3

/ ivasallay / 2 Comments

  • 203 is a composite number.
  • Prime factorization: 203 = 7 x 29
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 203 has exactly 4 factors.
  • Factors of 203: 1, 7, 29, 203
  • Factor pairs: 203 = 1 x 203 or 7 x 29
  • 203 has no square factors that allow its square root to be simplified. √203 ≈ 14.2478068

————————————————————————————————————–

2014-32 Level 3

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

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.

2014-32 Level 3 Factors

202 and Level 2

/ ivasallay / Leave a comment

  • 202 is a composite number.
  • Prime factorization: 202 = 2 x 101
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 202 has exactly 4 factors.
  • Factors of 202: 1, 2, 101, 202
  • Factor pairs: 202 = 1 x 202 or 2 x 101
  • 202 has no square factors that allow its square root to be simplified. √202 ≈ 14.2126704

——————————–

2014-32 Level 2

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

2014-32 Level 2 Factors

197 and Level 5

/ ivasallay / Leave a comment
  • 197 is a prime number.
  • Prime factorization: 197 is prime.
  • The exponent of prime number 197 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 197 has exactly 2 factors.
  • Factors of 197: 1, 197
  • Factor pairs: 197 = 1 x 197
  • 197 has no square factors that allow its square root to be simplified. √197 ≈ 14.0356688

How do we know that 197 is a prime number? If 197 were not a prime number, then it would be divisible by at least one prime number less than or equal to √197 ≈ 14. Since 197 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 197 is a prime number.

2014-31 Level 5

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-04

2014-31 Level 5 Logic

193 and Level 2

/ ivasallay / Leave a comment
  • 193 is a prime number.
  • Prime factorization: 193 is prime.
  • The exponent of prime number 193 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 193 has exactly 2 factors.
  • Factors of 193: 1, 193
  • Factor pairs: 193 = 1 x 193
  • 193 has no square factors that allow its square root to be simplified. √193 ≈ 13.89244

How do we know that 193 is a prime number? If 193 were not a prime number, then it would be divisible by at least one prime number less than or equal to √193 ≈ 13.9. Since 193 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 193 is a prime number.

2014-31 Level 2

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-04

2014-31 Level 2 Factors

192 and Level 1

/ ivasallay / Leave a comment
192 is a composite number.
Factor pairs: 192 = 1 x 192, 2 x 96, 3 x 64, 4 x 48, 6 x 32, 8 x 24, or 12 x 16
Factors of 192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
Prime factorization: 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3, which can also be written (2^6) x 3

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

2014-31 Level 1

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-04

2014-31 Level 1 Factors

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

 

190 and Level 5

/ ivasallay / Leave a comment
190 is a composite number.
Factor pairs: 190 = 1 x 190, 2 x 95, 5 x 38, 10 x 19
Factors of 190: 1, 2, 5, 10, 19, 38, 95, 190
Prime factorization: 190 = 2 x 5 x 19

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

2014-30 Level 5

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

2014-30 Level 5 Logic

 

189 and Level 4

/ ivasallay / Leave a comment
189 is a composite number.
Factor pairs: 189 = 1 x 189, 3 x 63, 7 x 27, 9 x 21
Factors of 189: 1, 3, 7, 9, 21, 27, 63, 189
Prime factorization: 189 = 3 x 3 x 3 x 7, which can also be written 189 = (3^3) x 7

——————————————————————————————————————–

2014-30 Level 4

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

2014-30 Level 4 Logic

188 and Level 3

/ ivasallay / Leave a comment
188 is a composite number.
Factor pairs: 188 = 1 x 188, 2 x 94, or 4 x 47
Factors of 188: 1, 2, 4, 47, 94, 188
Prime factorization: 188 = 2 x 2 x 47, which can be written 188 = (2^2) x 47

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

2014-30 Level 3

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

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.

2014-30 Level 3 Factors

187 and Level 2

/ ivasallay / Leave a comment
187 is a composite number.
Factor pairs: 187 = 1 x 187 or 11 x 17
Factors of 187: 1, 11, 17, 187
Prime factorization: 187 = 11 x 17

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

2014-30 Level 2

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

2014-30 Level 2 Factors