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 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
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:
Write the numbers from 1 to 12 in both the first column and the top row so that this puzzle functions like a multiplication table.
This week’s puzzles and last week’s solutions: 12 Factors 2014-04-07
84 is a composite number. 84 = 1 x 84, 2 x 42, 3 x 28, 4 x 21, 6 x 14, or 7 x 12. Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Prime factorization: 84 = 2 x 2 x 3 x 7 which can also be written 2² x 3 x 7.
Sometimes 84 is a clue in the FIND THE FACTORS 1 – 12 puzzles. Even though it has other factors, we only use 84 = 7 x 12 in the puzzles.
84 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 solve this puzzle!
84 is prominent in this cool pattern:
This week’s puzzles and last week’s solutions: 12 Factors 2014-04-07
How do we know that 83 is a prime number? If 83 were not a prime number, then it would be divisible by at least one prime number less than or equal to √83 ≈ 9.1. Since 83 cannot be divided evenly by 2, 3, 5, or 7, we know that 83 is a prime number.
83 is never a clue in the FIND THE FACTORS puzzles.
This week’s puzzles and last week’s solutions: 10 Factors 2014-03-31
82 is a composite number. 82 = 1 x 82 or 2 x 41. Factors of 82: 1, 2, 41, 82. Prime factorization: 82 = 2 x 41.
82 is never a clue in the FIND THE FACTORS puzzles.
Start with 82 and go backwards to 1
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…this number is prime!
— Fermat’s Library (@fermatslibrary) January 5, 2023
This week’s puzzles and last week’s solutions: 10 Factors 2014-03-31
81 is a composite number and is 9 squared. 81 = 1 x 81, 3 x 27, or 9 x 9. Factors of 81: 1, 3, 9, 27, 81. Prime factorization: 81 = 3 x 3 x 3 x 3 which can also be written 3⁴.
Since √81 = 9, a whole number, 81 is a perfect square.
Sometimes 81 is a clue in the FIND THE FACTORS puzzles. Even though it has other factors, the only multiplication fact we use is 9 x 9 = 81.
WordPress measures how many posts are written about certain topics each month and then they publish their findings. The results for March were published in the march-hot-list/. Cat lovers were informed, “your beloved felines yet again got trounced by their canine frenemies. Dogs: 10,589; cats: 6,401. Is that a big, defiant “meow” we hear? Maybe you’ll do better in April.”
I have two sisters who truly love their cats. Although I personally prefer neither pet over the other, I hate to see cats so clearly in the “underdog” role. Today’s puzzle looks a teeny tiny bit like the head of a cat, so I’m tagging it with the word “cats.” Of course, this post alone will not be enough to make much of a difference in April’s statistics.
This week’s puzzles and last week’s solutions: 10 Factors 2014-03-31
80 is a composite number. 80 = 1 x 80, 2 x 40, 4 x 20, 5 x 16, and 8 x 10. Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. Prime factorization: 80 = 2 x 2 x 2 x 2 x 5 which can also be written 80 = 2⁴ x 5.
Sometimes 80 is a clue in the FIND THE FACTORS puzzles. Even though it has other factors, the only multiplication fact we use is 8 x 10 = 80.
This week’s puzzles and last week’s solutions: 10 Factors 2014-03-31
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:
This week’s puzzles and last week’s solutions: 10 Factors 2014-03-31
77 is a composite number. 77 = 1 x 77 or 7 x 11. Factors of 77: 1, 7, 11, 77. Prime factorization: 77 = 7 x 11.
Sometimes 77 is a clue in the FIND THE FACTORS 1 – 12 puzzles. Even though it has other factors, the puzzle only uses 7 x 11 = 77.
