number puzzle

153 and Level 5

/ ivasallay / Leave a comment

 

153 is a composite number and so much more!
Factor pairs: 153 = 1 x 153, 3 x 51, or 9 x 17.
Factors of 153: 1, 3, 9, 17, 51, 153.
Prime factorization: 153 = 3 x 3 x 17, which can be written (3^2) x 17.

I first learned that 153 = 1³ + 5³ + 3³ when I read mystery-numbers-370-153. This “St. Peter’s fish” number is so specific that it baffles scholars and students of the Bible.

Is the fact that 153 = 3•51 just as mysterious?

 

2014-24 Level 5

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

2014-24 Level 5 Logic

152 and Level 4

/ ivasallay / Leave a comment
152 is a composite number.
Factor pairs: 152 = 1 x 152, 2 x 76, 4 x 38, or 8 x 19
Factors of 152: 1, 2, 4, 8, 19, 38, 76, 152
Prime factorization: 152 = 2 x 2 x 2 x 19, which can be written (2^3) x 19

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2014-24 Level 4

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

2014-24 Level 4 Logic

150 and Level 3

/ ivasallay / 1 Comment

Today’s Puzzle:

2014-24 Level 3

Factors of 150:

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

150 is a composite number.
Factor pairs:150 = 1 x 150, 2 x 75, or 3 x 50, 5 x 30, 6 x 25, or 10 x 15
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Prime factorization: 150 = 2 x 3 x 5 x 5, which can also be written 150 = 2 x 3 x (5^2)

Sum-Difference Puzzle:

6 has two factor pairs. One of those factor pairs adds up to 5, and the other one subtracts to 5. Can you place those factors in the proper boxes to complete the first puzzle?

150 has six factor pairs. One of those factor pairs adds up to 25, and another one subtracts to 25. If you can identify those factor pairs, then you can complete the second puzzle!

The second puzzle is really just the first puzzle in disguise.  Why would I say that?

More About the Number 150:

I verified this for myself:

A Logical Way to Solve Today’s Puzzle:

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.

2014-24 Level 3 Factors

 

149 and Level 2

/ ivasallay / Leave a comment
  • 149 is a prime number.
  • Prime factorization: 149 is prime.
  • The exponent of prime number 149 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 149 has exactly 2 factors.
  • Factors of 149: 1, 149
  • Factor pairs: 149 = 1 x 149
  • 149 has no square factors that allow its square root to be simplified. √149 ≈ 12.2065556

How do we know that 149 is a prime number? If 149 were not a prime number, then it would be divisible by at least one prime number less than or equal to √149 ≈ 12.2. Since 149 cannot be divided evenly by 2, 3, 5, 7, or 11, we know that 149 is a prime number.

2014-24 Level 2

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

2014-24 Level 2 Factors

148 and Level 1

/ ivasallay / Leave a comment
148 is a composite number.
Factor pairs:148 = 1 x 148, 2 x 74, or 4 x 37
Factors of 148: 1, 2, 4, 37, 74, 148
Prime factorization: 148 = 2 x 2 x 37, which can also be written 148 = (2^2) x 37

2014-24 Level 1

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

2014-24 Level 1 Factors

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

146 and Level 5

/ ivasallay / Leave a comment

146 is a composite number. Factor pairs: 146 = 1 x 146 or 2 x 73. Factors of 146: 1, 2, 73, 146. Prime factorization: 146 = 2 x 73.

2014-23 Level 5

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

2014-23 Level 5 Logic

145 and Level 4

/ ivasallay / 2 Comments

145 is a composite number. Factor pairs: 145 = 1 x 145, 5 x 29. Factors of 145: 1, 5, 29, 145. Prime factorization: 145 = 5 x 29.

 

2014-23 Level 4

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

2014-23 Level 4 Logic

144 and Level 3

/ ivasallay / Leave a comment

144 is a composite number and a perfect square. Factor pairs: 144 = 1 x 144, 2 x 72, 3 x 48, 4 x 36, 6 x 24, 8 x 18, 9 x 16, 12 x 12. Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Prime factorization: 144 = 2 x 2 x 2 x 2 x 3 x 3, which can also be written 144 = (2^4) x (3^2).

144 is the largest clue that appears in the FIND THE FACTORS 1 – 12 puzzles. For the puzzles in which it is a clue, always use 12 x 12 as the factors.


2014-23 Level 3

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

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.

2014-23 Level 3 Factors

 

143 and Level 2

/ ivasallay / Leave a comment

143 is a composite number. Factor pairs: 143 = 1 x 143 or 11 x 13. Factors of 143: 1, 11, 13, 143. Prime factorization: 143 = 11 x 13.

143 is never a clue in the FIND THE FACTORS 1-10 or 1-12 puzzles.

2014-23 Level 2

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

2014-23 Level 2 Factors