| 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
Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-06-16
| 150 is a composite number. |
| Factor pairs:150 = 1 x 150, 2 x 75, or 3 x 50, 5 x 30, 6 x 25, or 10 x 15 |
| Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 |
| Prime factorization: 150 = 2 x 3 x 5 x 5, which can also be written 150 = 2 x 3 x (5^2) |
6 has two factor pairs. One of those factor pairs adds up to 5, and the other one subtracts to 5. Can you place those factors in the proper boxes to complete the first puzzle?
150 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 complete the second puzzle!
The second puzzle is really just the first puzzle in disguise. Why would I say that?
Shiver in awe. Mathematics.
“150” pic.twitter.com/jxANbj9Ig1
— Cliff Pickover (@pickover) February 25, 2024
I verified this for myself:
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.
| 148 is a composite number. |
| Factor pairs:148 = 1 x 148, 2 x 74, or 4 x 37 |
| Factors of 148: 1, 2, 4, 37, 74, 148 |
| Prime factorization: 148 = 2 x 2 x 37, which can also be written 148 = (2^2) x 37 |
Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-06-16
| 147 is a composite number. |
| Factor pairs:147 = 1 x 147, 3 x 49, or 7 x 21. |
| Factors of 147: 1, 3, 7, 21, 49, 147. |
| Prime factorization: 147 = 3 x 7 x 7, which can also be written 147 = 3 x (7^2). |
Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-09
146 is a composite number. Factor pairs: 146 = 1 x 146 or 2 x 73. Factors of 146: 1, 2, 73, 146. Prime factorization: 146 = 2 x 73.
Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-09
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
144 is a composite number and a perfect square. Factor pairs: 144 = 1 x 144, 2 x 72, 3 x 48, 4 x 36, 6 x 24, 8 x 18, 9 x 16, 12 x 12. Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Prime factorization: 144 = 2 x 2 x 2 x 2 x 3 x 3, which can also be written 144 = (2^4) x (3^2).
144 is the largest clue that appears in the FIND THE FACTORS 1 – 12 puzzles. For the puzzles in which it is a clue, always use 12 x 12 as the factors.
Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-09
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.
143 is a composite number. Factor pairs: 143 = 1 x 143 or 11 x 13. Factors of 143: 1, 11, 13, 143. Prime factorization: 143 = 11 x 13.
143 is never a clue in the FIND THE FACTORS 1-10 or 1-12 puzzles.
Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-09
142 is a composite number. Factor pairs: 142 = 1 x 142 or 2 x 71. Factors of 142: 1, 2, 71, 142. Prime factorization: 142 = 2 x 71.
142 is never a clue in the FIND THE FACTORS puzzles.
Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-09
141 is a composite number. Factor pairs: 141 = 1 x 141 or 3 x 47. Factors of 141: 1, 3, 47, 141. Prime factorization: 141 = 3 x 47.
141 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
