Level 3 Puzzle

182 and Level 3

/ ivasallay / Leave a comment
182 is a composite number.
Factor pairs: 182 = 1 x 182, 2 x 91, 7 x 26, or 13 x 14
Factors of 182: 1, 2, 7, 13, 14, 26, 91, 182
Prime factorization: 182 = 2 x 7 x 13

Notice this for 182: 18 – (2 x 2) = 18 – 4 = 14, a multiple of 7, so 182 can be evenly divided by 7.


2014-29 Level 3
Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-07-21

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.

2014-29 Level 3 Factors

176 and Level 3

/ ivasallay / Leave a comment
176 is a composite number.
Factor pairs: 176 = 1 x 176, 2 x 88, 4 x 44, 8 x 22, or 11 x 16
Factors of 176: 1, 2, 4, 8, 11, 16, 22, 44, 88, 176
Prime factorization: 176 = 2 x 2 x 2 x 2 x 11 which can be written (2^4) x 11.

2014-28 Level 3

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

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.

2014-28 Level 3 Factors

170 and Level 3

/ ivasallay / Leave a comment
170 is a composite number.
Factor pairs: 170 = 1 x 170, 2 x 85, 5 x 34, or 10 x 17
Factors of 170: 1, 2, 5, 10, 17, 34, 85, 170
Prime factorization: 170 = 2 x 5 x 17

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2014-27 Level 3

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

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.

2014-27 Level 3 Factors

163 and Level 3

/ ivasallay / 2 Comments
  • 163 is a prime number.
  • Prime factorization: 163 is prime.
  • The exponent of prime number 163 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 163 has exactly 2 factors.
  • Factors of 163: 1, 163
  • Factor pairs: 163 = 1 x 163
  • 163 has no square factors that allow its square root to be simplified. √163 ≈ 12.7671

How do we know that 163 is a prime number? If 163 were not a prime number, then it would be divisible by at least one prime number less than or equal to √163 ≈ 12.8. Since 163 cannot be divided evenly by 2, 3, 5, 7, or 11, we know that 163 is a prime number.

2014-26 Level 3

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

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.

2014-26 Level 3 Factors

157 and Level 3

/ ivasallay / Leave a comment
  • 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

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

 

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

 

136 and Level 3

/ ivasallay / Leave a comment

136 is a composite number. 136 = 1 x 136, 2 x 68, 4 x 34, or 8 x 17. Factors of 136: 1, 2, 4, 8, 17, 34, 68, 136. Prime factorization: 136 = 2 x 2 x 2 x 17, which can also be written 136 = 2³ x 17.

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

2014-22 Level 3

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

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.

2014-22 Level 3 Factors

130 and Level 3

/ ivasallay / Leave a comment

130 is a composite number. 130 = 1 x 130, 2 x 65, 5 x 26, or 10 x 13. Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130. Prime factorization: 130 = 2 x 5 x 13.

130 is never a clue in the  FIND THE FACTORS 1 – 10 or 1 – 12 puzzles.

2014-21 Level 3

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

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:

2014-21 Level 3 Factors

124 and Level 3

/ ivasallay / Leave a comment

124 is a composite number. 124 = 1 x 124, 2 x 62, or 4 x 31. Factors of 124: 1, 2, 4, 31, 62, 124. Prime factorization:124 = 2 x 2 x 31, which can also be written 124 = 2² x 31.

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

2014-20 Level 3

Excel file of this week’s puzzles and last week’s factors: 12 Factors 2014-05-19

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:

2014-20 Level 3 Factors