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.

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.

135 is a composite number. 135 = 1 x 135, 3 x 45, 5 x 27, or 9 x 15. Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135. Prime factorization: 135 = 3 x 3 x 3 x 5, which can also be written 135 = 3³ x 5.

1 + 3 + 5 = 9. Nine is a multiple of both 3 and 9, so this quick divisibility trick lets us know that both 3 and 9 are factors of 135.

135 = 1⁵ x 3³ x 5¹. Click 135 to learn two other ways to have 1, 3, 5 on both sides of the equal sign.

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

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

134 is a composite number. 134 = 1 x 134 or 2 x 67. Factors of 134: 1, 2, 67, 134. Prime factorization: 134 = 2 x 67.

Here is a Complicated but fascinating number fact from Wikipedia that involves 134 on BOTH sides of the equation:

Notice that each term has an 8 sub-scripted on the left side of the C and either 1, 3, or 4 sub-scripted on the right side of the C. If you do all the division, multiplication and addition, you will discover that  ₈C₁ + ₈C₃ + ₈C₄ = 8 + 56 + 70 = 134.

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

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

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.

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

132 is a composite number. 132 = 1 x 132, 2 x 66, 3 x 44, 4 x 33, 6 x 22, or 11 x 12. Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132. Prime factorization: 132 = 2 x 2 x 3 x 11, which can also be written 132 = 2² x 3 x 11.

Taking the factor pair with the largest square number factor, we get √132 = (√4)(√33) = 2√33 ≈ 11.489

When 132 is a clue in the FIND THE FACTORS  1 – 12 puzzles, always use 11 and 12 as the factors.

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This puzzle reminds me of a couple of hourglass scenes from The Wizard of Oz that can be found in the middle of the page here. Yes, I know my hourglass is about the size of an egg timer, but hurry and solve the puzzle! Dorothy’s life could depend on it.

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