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.
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
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.
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:
129 is a composite number. 129 = 1 x 129 or 3 x 43. Factors of 129: 1, 3, 43, 129. Prime factorization: 129 = 3 x 43.
2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 129, thus 129 is the sum of the first 10 prime numbers.
129 is never a clue in the FIND THE FACTORS puzzles.
Excel file of puzzles and previous week’s solutions: 10 Factors 2014-05-26
128 is a composite number. 128 = 1 x 128, 2 x 64, 4 x 32, or 8 x 16. Factors of 128: 1, 2, 4, 8, 16, 32, 64, 128. Prime factorization: 128 = 2×2×2×2×2×2×2 which can be written 128 = 2⁷
128 is never a clue in the FIND THE FACTORS puzzles.
Excel file of puzzles and last week’s solutions: 10 Factors 2014-05-26
126 is a composite number. 126 = 1 x 126, 2 x 63, 3 x 42, 6 x 21, 7 x 18, or 9 x 14. Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. Prime factorization: 126 = 2 x 3 x 3 x 7, which can also be written 2 x 3² x 7.
Thinking process using divisibility tricks to find the factor pairs of 126 quickly:
√126 is irrational and approximately equal to 11.22. Every factor pair of 126 will have one factor less than 11.22 and one factor greater than 11.22, and we will find both factors in each pair at the same time. The following integers are less than 11.22. Are they factors of 126?
From this thinking process we conclude that the factor pairs of 126 are 1 x 126, 2 x 63, 3 x 42, 6 x 21, 7 x 18, and 9 x 14.
126 is never a clue in the FIND THE FACTORS puzzles.
Today’s puzzle might be the most difficult level 5 puzzle I have ever published, so if you have never solved a level 5 or level 6 puzzle before, you probably don’t want to start with this one.
Excel file of this week’s puzzles and last week’s factors: 12 Factors 2014-05-19
125 is a composite number. 125 = 1 x 125 or 5 x 25. Factors of 125: 1, 5, 25, 125. Prime factorization: 125 = 5 x 5 x 5, which can also be written 125 = 5³.
125 is never a clue in the FIND THE FACTORS puzzles.
Placing the last few factors on this Level 4 puzzle may be a bit trickier than usual. As always, use logic, not guessing and checking, to find its one and only solution. Good luck!
Excel file of this week’s puzzles and last week’s factors: 12 Factors 2014-05-19
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.
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:
123 is a composite number. 123 = 1 x 123 or 3 x 41. Factors of 123: 1, 3, 41, 123. Prime factorization: 123 = 3 x 41.
123 is never a clue in the FIND THE FACTORS puzzles.
Excel file of this week’s puzzles and last week’s factors: 12 Factors 2014-05-19
122 is a composite number. 122 = 1 x 122 or 2 x 61. Factors of 122: 1, 2, 61, 122. Prime factorization: 122 = 2 x 61.
122 is never a factor in the FIND THE FACTORS puzzles.
122 is the sum of two squares:
11² + 1² = 122
122 is the hypotenuse of a Pythagorean triple:
22-120-122 calculated from 2(11)(1), 11² – 1², 11² + 1²
Excel file of this week’s puzzles and last week’s factors: 12 Factors 2014-05-19
