Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-04
| 189 is a composite number. |
| Factor pairs: 189 = 1 x 189, 3 x 63, 7 x 27, 9 x 21 |
| Factors of 189: 1, 3, 7, 9, 21, 27, 63, 189 |
| Prime factorization: 189 = 3 x 3 x 3 x 7, which can also be written 189 = (3^3) x 7 |
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Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-07-28
| 183 is a composite number. |
| Factor pairs: 183 = 1 x 183 or 3 x 61 |
| Factors of 183: 1, 3, 61, 183 |
| Prime factorization: 183 = 3 x 61 |
Notice this for 183: 1 + 8 + 3 = 12 which is a multiple of 3, so 183 is also a multiple of 3.
Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-07-21
| 177 is a composite number. |
| Factor pairs: 177 = 1 x 177, 3 x 59 |
| Factors of 177: 1, 3, 59, 177 |
| Prime factorization: 177 = 3 x 59 |
Here is a magic square made entirely of prime numbers:
What number do you get when you add up the numbers of any one of its rows, columns, or diagonals?
According to Wikipedia, you can’t get a smaller magic sum than 177 when all the numbers in the magic square are prime numbers. Wolfram MathWorld has several Prime Magic Squares of various dimensions up to 13 × 13. Two of the squares include the number 1, which is not a prime number but is sometimes permitted to be in a prime magic square because it is not a composite number.
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Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-07-14
| 164 is a composite number. |
| Factor pairs: 164 = 1 x 164, 2 x 82, or 4 x 41 |
| Factors of 164: 1, 2, 4, 41, 82, 164 |
| Prime factorization: 164 = 2 x 2 x 41, which can be written 164 = (2^2) x 4 |
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Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-06-30
| 158 is a composite number. |
| Factor pairs: 158 = 1 x 158 or 2 x 79 |
| Factors of 158: 1, 2, 79, 158 |
| Prime factorization: 158 = 2 x 79 |
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Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23
| 152 is a composite number. |
| Factor pairs: 152 = 1 x 152, 2 x 76, 4 x 38, or 8 x 19 |
| Factors of 152: 1, 2, 4, 8, 19, 38, 76, 152 |
| Prime factorization: 152 = 2 x 2 x 2 x 19, which can be written (2^3) x 19 |
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Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-06-16
145 is a composite number. Factor pairs: 145 = 1 x 145, 5 x 29. Factors of 145: 1, 5, 29, 145. Prime factorization: 145 = 5 x 29.
El factorial de n se define como el producto de todos los enteros positivos desde 1 hasta n, por ejemplo:
5! = 5 · 4 · 3 · 2 · 1
Y por convención 0! = 1
Un factorion es un número que es igual a la suma de los factoriales de sus cifras. Solamente existen cuatro factoriones: pic.twitter.com/dtUQxv3RG3
— fun with functions (@funfunfunctions) April 5, 2021
Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-09
How do we know that 137 is a prime number? If 137 were not a prime number, then it would be divisible by at least one prime number less than or equal to √137 ≈ 11.7. Since 137 cannot be divided evenly by 2, 3, 5, 7, or 11, we know that 137 is a prime number.
137 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
How do we know that 131 is a prime number? If 131 were not a prime number, then it would be divisible by at least one prime number less than or equal to √131 ≈ 11.4. Since 131 cannot be divided evenly by 2, 3, 5, 7, or 11, we know that 131 is a prime number.
131 is never a clue in the FIND THE FACTORS puzzles.
Excel file of puzzles and previous week’s solutions: 10 Factors 2014-05-26
