95 is a composite number. 95 = 1 x 95 or 5 x 19. The factors of 95: 1, 5, 19, 95. Prime factorization: 95 = 5 x 19.
95 is never a clue in the FIND THE FACTORS puzzles.
This week’s puzzles and last week’s solutions: 10 Factors 2014-04-14
94 and Level 5
94 is a composite number. 94 = 1 x 94 or 2 x 47. The factors of 94: 1, 2, 47, 94. Prime factorization: 94 = 2 x 47.
94 is never a clue in the FIND THE FACTORS puzzles.
This week’s puzzles and last week’s solutions: 10 Factors 2014-04-14
93 and Level 4
93 is a composite number. 93 = 1 x 93 or 3 x 31. The factors of 93: 1, 3, 31, 93. Prime factorization: 93 = 3 x 31.
93 is never a clue in the FIND THE FACTORS puzzles.
This week’s puzzles and last week’s solutions: 10 Factors 2014-04-14
92 and Level 3
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.
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:
91 and River crossings
The age-old river crossing puzzle is humorously presented and beautifully illustrated with manipulatives that can easily be printed, cutout, and assembled. It will be a winner with children and adults alike.
The puzzle is this: The farmer needs to get a bag of corn, a chicken, and a fox across a river. The boat is small and can only hold the farmer and one other thing at a time. The farmer cannot ever leave the chicken with either the corn or the fox because one of them will be eaten before he returns. He can take several trips across the river, but how does he get all three across?
Pat’s Blog gives a history of the famous puzzle and its variations, and TV Tropes gives the solution to the puzzle here.
91 is a composite number. 91 = 1 x 91 or 7 x 13. Factors of 91: 1, 7, 13, 91. Prime factorization: 91 = 7 x 13.
91 is never a clue in the FIND THE FACTORS puzzles.
91 is prominent in this cool pattern:
90 and Level 2
A right angle is 90°.
Pythagorean triples are three whole number sides that form a right triangle. In one such triangle, 54-72-90, the longest side, 90, is opposite the 90° angle!
In seven other right triangles, side 90 is adjacent to the 90° angle:
- 48-90-102
- 56-90-106
- 90-120-150
- 90-216-234
- 90-400-410
- 90-672-678
- 90-2024-2026
90 is a composite number. 90 = 1 x 90, 2 x 45, 3 x 30, 5 x 18, 6 x 15, and 9 x 10. Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. Prime factorization: 90 = 2 × 3 × 3 × 5 which can also be written 2 × 3² × 5.
Sometimes 90 is a clue in the FIND THE FACTORS 1 – 12 puzzles. Even though it has other factors, we only use 90 = 9 x 10 in the puzzles.
This week’s puzzles and last week’s solutions: 10 Factors 2014-04-14
89 and Level 1
- 89 is a prime number.
- Prime factorization: 89 is prime.
- The exponent of prime number 89 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 89 has exactly 2 factors.
- Factors of 89: 1, 89
- Factor pairs: 89 = 1 x 89
- 89 has no square factors that allow its square root to be simplified. √89 ≈ 9.43398
How do we know that 89 is a prime number? If 89 were not a prime number, then it would be divisible by at least one prime number less than or equal to √89 ≈ 9.4. Since 89 cannot be divided evenly by 2, 3, 5, or 7, we know that 89 is a prime number.
89 is never a clue in the FIND THE FACTORS puzzles.
This week’s puzzles and last week’s solutions: 10 Factors 2014-04-14
88 and April Showers
88 is a composite number. 88 = 1 x 88, 2 x 44, 4 x 22, and 8 x 11. Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88. Prime factorization: 88 = 2 x 2 x 2 x 11 which can also be written 88 = 2³ x 11.
Sometimes 88 is a clue in the FIND THE FACTORS 1 – 12 puzzles. Even though it has other factors, we only use 88 = 8 x 11 in the puzzles.
This week’s puzzles and last week’s solutions: 12 Factors 2014-04-07
Getting started logically on this puzzle is a little complicated, and I may have abbreviated too much in the chart below, so here is an explanation in regular English: The clue 14 has to use one of the 2s, so the clue 4 cannot be 2 x 2. Since 4 will be 4 x 1, and thus using one of the 4s, 16 cannot be 4 x 4, but must be 2 x 8. Since 14 and 16 use both of the 2s, 10 cannot be 2 x 5 and must be 1 x 10. Finally that means that the only clue on the puzzle that has 5 as the factor is 35, so the blank space must belong to 5 as well.
87 and Level 5
8 + 7 = 15, a multiple of 3, so 87 is divisible by 3.
87 is a composite number. 87 = 1 x 87 or 3 x 29. Factors of 87: 1, 3, 29, 87. Prime factorization: 87 = 3 x 29.
87 is never a clue in the FIND THE FACTORS puzzles.
This week’s puzzles and last week’s solutions: 12 Factors 2014-04-07
86 and Level 4
86 is a composite number. 86 = 1 x 86 or 2 x 43. Factors of 86: 1, 2, 43, 86. Prime factorization: 86 = 2 x 43.
86 is never a clue in the FIND THE FACTORS puzzles.
This week’s puzzles and last week’s solutions: 12 Factors 2014-04-07
