Level 3 Puzzle

118 and Level 3

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118  is a composite number. 118 = 1 x 118 or 2 x 59. Factors of 118: 1, 2, 59, 118. Prime factorization: 118 = 2 x 59.

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

2014-19 Level 3

Excel file of puzzles and the previous week’s factors: 10 Factors 2014-05-12

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:

2014-19 Level 3 factors

110 and Level 3

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110 is a composite number. 110 = 1 x 110, 2 x 55, 5 x 22, or 10 x 11. Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110. Prime factorization: 110 = 2 x 5 x 11.

When 110 is a clue in the FIND THE FACTORS 1 – 12 puzzles, use 10 and 11 as the factors.

2014-18 Level 3

Excel file of puzzles and the previous week’s solutions: 12 Factors 2014-05-05

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:

2014-18 Level 3 Factors

104 and Level 3

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104 is a composite number. 104 = 1 x 104, 2 x 52, 4 x 26, or 8 x 13. Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104. Prime factorization: 104 = 2 x 2 x 2 x 13, which can also be written 2³ x 13.

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

2014-17 Level 3

The week’s puzzles and the previous week’s solutions: 10 Factors 2014-04-28

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 and factor 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 table one row at a time as you go:

2014-17 Level 3 factors

98 and What Do You Do When You Get to the End of a Shoe Lace?

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In the past finding the factors for a level 3 puzzle has been like lacing an entire shoe with only one end of the lace. Today’s puzzle is slightly more difficult because that end of the lace gets cut off in the middle of the puzzle, and the other end of the lace has to be used to find the rest of the factors. Level 3 is meant to be a bridge between the easier levels and the higher leveled puzzles, and those laces get cut off in the higher leveled puzzles all the time. Good luck with this level 3 puzzle! I’m sure you can still find all the factors!

2014-16 Level 3

This week’s puzzles and last week’s solutions: 12 Factors 2014-04-21

98 is a composite number. 98 = 1 x 98, 2 x 49, or 7 x 14. Factors of 98: 1, 2, 7, 14, 49, 98. Prime factorization: 98 = 2 x 7 x 7, which can also be written 98 = 2 x 7²

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

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 and factor 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 table one row at a time as you go:

2014-16 Level 3 Factors

92 and Level 3

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92 is a composite number. 92 = 1 x 92, 2 x 46, or 4 x 23.  Factors of 92: 1, 2, 4, 23, 46, 92. Prime factorization: 92 = 2 x 2 x 23 which can also be written 92 = 2² x 23.

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

2014-15 Level 3

This week’s puzzles and last week’s solutions: 10 Factors 2014-04-14

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 and factor 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 table one row at a time as you go:

2014-15 Level 3 Factors

85 and Level 3

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2014-14 Level 3

This week’s puzzles and last week’s solutions: 12 Factors 2014-04-07

85 is a composite number. 85 = 1 x 85 or 5 x 17. Factors of 85: 1, 5, 17, 85. Prime factorization: 85 = 5 x 17.

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

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 and factor 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 table one row at a time as you go:

2014-14 Level 3 Factors

79 and Level 3

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2014-13 Level 3

This week’s puzzles and last week’s solutions: 10 Factors 2014-03-31

  • 79 is a prime number.
  • Prime factorization: 79 is prime.
  • The exponent of prime number 79 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 79 has exactly 2 factors.
  • Factors of 79: 1, 79
  • Factor pairs: 79 = 1 x 79
  • 79 has no square factors that allow its square root to be simplified. √79 ≈ 8.8881944

How do we know that 79 is a prime number? If 79 were not a prime number, then it would be divisible by at least one prime number less than or equal to √79 ≈ 8.8. Since 79 cannot be divided evenly by 2, 3, 5, or 7, we know that 79 is a prime number.

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

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 and factor 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 table one row at a time as you go:

2014-13 Level 3 Factors

71 and Level 3

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2014-12 Level 3

This week’s puzzles for you to solve

Here’s a little about the number 71:

  • 71 is a prime number.
  • Prime factorization: 71 is prime.
  • The exponent of prime number 71 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 71 has exactly 2 factors.
  • Factors of 71: 1, 71
  • Factor pairs: 71 = 1 x 71
  • 71 has no square factors that allow its square root to be simplified. √71 ≈ 8.4261

How do we know that 71 is a prime number? If 71 were not a prime number, then it would be divisible by at least one prime number less than or equal to √71 ≈ 8.4. Since 71 cannot be divided evenly by 2, 3, 5, or 7, we know that 71 is a prime number.

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

A Logical Approach to the Solution of the puzzle: Find the column or row with two clues and find their common factor. Write the corresponding factors in the factor column and factor 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 table as you go:

2014-12 Level 3 Factors

57 and Cupid’s arrow is on its way!

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57 is a composite number. 57 = 1 x 57 or 3 x 19. Factors of 57: 1, 3, 19, 57. Prime factorization: 57 = 3 x 19.

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

How do you feel about factoring?

If you will let Cupid hit you with this arrow, you might just fall in love with factors.

Factoring is very important in many levels of mathematics, so enjoying it can be a very good thing.

2014-05 Level 3

I love factoring. I hope you will let Cupid’s arrow hit you so you will love factoring, too.

This week’s puzzles are available in an excel file here. If you have a spreadsheet program on your computer, you can access it. If you enable editing in excel, you can type your answers directly onto the puzzle, and you can also easily print the puzzles.

The factors for last week’s level 3 Puzzle:

2014-04 Level 3 Answer

Here’s how last week’s puzzle was solved:

2014-04 L-3 steps

49 and V is for Victory Puzzle

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49 is a composite number, and it is 7 squared. 49 = 1 x 49 or 7 x 7. Factors of 49: 1, 7, 49. Prime factorization: 49 = 7 x 7 which can also be written 49 = 7².

Since √49 = 7, a whole number, 49 is a perfect square. 

Whenever 49 is a clue in the FIND THE FACTOR puzzles, write 7 in both the corresponding factor column and factor row.

Level 3 is the first level of the higher level FIND THE FACTORS puzzles. For many people going from level 2 to level 4 would be too overwhelming. Level 3 is a bridge between those two levels and allows a person to move on from the lower levels and victoriously solve a little more difficult puzzle. V is for that victory.

Level 3 puzzles are designed to be solved starting from a row or column at the top of the puzzle with 2 clues. First find the common factor of those two clues that will allow you to write only numbers from 1 to 10 in the first column of the puzzle. Then factor row by row to the bottom of the puzzle making sure each number from 1 to 12 is written only once in both the factor row and the factor column. You will notice a rhythm for the answers as you work.

2014-04 Level 3

 

This week’s puzzles are available in an excel file here. If you have a spreadsheet program on your computer, you can access it. If you enable editing in excel, you can type your answers directly onto the puzzle, and you can also easily print the puzzles. May you be victorious in your efforts!

Here are the factors to last week’s level 3 puzzle:

2014-03 Level 3 Answer

 

This puzzle was solved starting with the column with 2 clues near the top of the puzzle and then factoring row by row until we reached the bottom of the puzzle.