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
Multiplication table
85 and 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:
84 and Level 2
Today’s Puzzle:
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
Factors of 84:
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.
Sum-Difference Puzzle:
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!
More about the Number 84:
84 is prominent in this cool pattern:
Answer to This Week’s Puzzle:
83 and Level 1
This week’s puzzles and last week’s solutions: 12 Factors 2014-04-07
- 83 is a prime number.
- Prime factorization: 83 is prime.
- The exponent of prime number 83 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 83 has exactly 2 factors.
- Factors of 83: 1, 83
- Factor pairs: 83 = 1 x 83
- 83 has no square factors that allow its square root to be simplified. √83 ≈ 9.11043
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.
82 and Level 6
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
8281807978777675747372717069686 7666564636261605958575655545352 5150494847464544434241403938373 6353433323130292827262524232221 2019181716151413121110987654321
…this number is prime!
— Fermat’s Library (@fermatslibrary) January 5, 2023
81 and Level 5
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.
80 and A Puzzled Cat
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.
79 and 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:
77 and Level 2
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.
76 and Level 1
This week’s puzzles and last week’s solutions: 10 Factors 2014-03-31
76 is a composite number. 76 = 1 x 76, 2 x 38, or 4 x 19. Factors of 76: 1, 2, 4, 19, 38, 76, Prime factorization: 76 = 2 x 2 x 19, which can also be written 2² x 19.
76 is never a clue in the FIND THE FACTORS puzzles.
