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You can put this solution on YOUR website!
Let's make a table. The first column represents the number X. For example in row 8, we have X = 8. We're finding the divisors of the number X = 8. The same applies for the other rows as well. \r
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\n" ); document.write( "\n" ); document.write( "The second column represents the number of divisors (eg: the number 7 has 2 divisors, so a 2 will go in the second column in row 7). \r
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\n" ); document.write( "\n" ); document.write( "The third column represents the actual list of divisors so you can count yourself to check the value in the second column.\r
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\n" ); document.write( "\n" ); document.write( "We'll stop once we have the second column have a \"7\" in it\r
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| X | number of divisors for number X | list of divisors for number X |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 1,2 |
| 3 | 2 | 1,3 |
| 4 | 3 | 1,2,4 |
| 5 | 2 | 1,5 |
| 6 | 4 | 1,2,3,6 |
| 7 | 2 | 1,7 |
| 8 | 4 | 1,2,4,8 |
| 9 | 3 | 1,3,9 |
| 10 | 4 | 1,2,5,10 |
| 11 | 2 | 1,11 |
| 12 | 6 | 1,2,3,4,6,12 |
| 13 | 2 | 1,13 |
| 14 | 4 | 1,2,7,14 |
| 15 | 4 | 1,3,5,15 |
| 16 | 5 | 1,2,4,8,16 |
| 17 | 2 | 1,17 |
| 18 | 6 | 1,2,3,6,9,18 |
| 19 | 2 | 1,19 |
| 20 | 6 | 1,2,4,5,10,20 |
| 21 | 4 | 1,3,7,21 |
| 22 | 4 | 1,2,11,22 |
| 23 | 2 | 1,23 |
| 24 | 8 | 1,2,3,4,6,8,12,24 |
| 25 | 3 | 1,5,25 |
| 26 | 4 | 1,2,13,26 |
| 27 | 4 | 1,3,9,27 |
| 28 | 6 | 1,2,4,7,14,28 |
| 29 | 2 | 1,29 |
| 30 | 8 | 1,2,3,5,6,10,15,30 |
| 31 | 2 | 1,31 |
| 32 | 6 | 1,2,4,8,16,32 |
| 33 | 4 | 1,3,11,33 |
| 34 | 4 | 1,2,17,34 |
| 35 | 4 | 1,5,7,35 |
| 36 | 9 | 1,2,3,4,6,9,12,18,36 |
| 37 | 2 | 1,37 |
| 38 | 4 | 1,2,19,38 |
| 39 | 4 | 1,3,13,39 |
| 40 | 8 | 1,2,4,5,8,10,20,40 |
| 41 | 2 | 1,41 |
| 42 | 8 | 1,2,3,6,7,14,21,42 |
| 43 | 2 | 1,43 |
| 44 | 6 | 1,2,4,11,22,44 |
| 45 | 6 | 1,3,5,9,15,45 |
| 46 | 4 | 1,2,23,46 |
| 47 | 2 | 1,47 |
| 48 | 10 | 1,2,3,4,6,8,12,16,24,48 |
| 49 | 3 | 1,7,49 |
| 50 | 6 | 1,2,5,10,25,50 |
| 51 | 4 | 1,3,17,51 |
| 52 | 6 | 1,2,4,13,26,52 |
| 53 | 2 | 1,53 |
| 54 | 8 | 1,2,3,6,9,18,27,54 |
| 55 | 4 | 1,5,11,55 |
| 56 | 8 | 1,2,4,7,8,14,28,56 |
| 57 | 4 | 1,3,19,57 |
| 58 | 4 | 1,2,29,58 |
| 59 | 2 | 1,59 |
| 60 | 12 | 1,2,3,4,5,6,10,12,15,20,30,60 |
| 61 | 2 | 1,61 |
| 62 | 4 | 1,2,31,62 |
| 63 | 6 | 1,3,7,9,21,63 |
| 64 | 7 | 1,2,4,8,16,32,64 |
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\n" ); document.write( "\n" ); document.write( "Things to notice
\n" ); document.write( "1) The prime numbers only have 2 divisors. This is always true because that's what a prime number is: a number divisible by itself and 1 (and no other number).
\n" ); document.write( "2) The perfect squares have an odd number of divisors while any other number has an even number of divisors. So because we want 7 divisors, this means that we could restrict ourselves to just looking at the perfect squares. It makes a much nicer table that is smaller\r
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| X | number of divisors for number X | list of divisors for number X |
|---|---|---|
| 1 | 1 | 1 |
| 4 | 3 | 1,2,4 |
| 9 | 3 | 1,3,9 |
| 16 | 5 | 1,2,4,8,16 |
| 25 | 3 | 1,5,25 |
| 36 | 9 | 1,2,3,4,6,9,12,18,36 |
| 49 | 3 | 1,7,49 |
| 64 | 7 | 1,2,4,8,16,32,64 |
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\n" ); document.write( "\n" ); document.write( "From either table, we see that the number 64 is the smallest positive integer that has exactly 7 positive divisors (or factors). Those divisors are 1,2,4,8,16,32,64\r
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\n" ); document.write( "\n" ); document.write( "-------------------------------------------------------\r
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\n" ); document.write( "\n" ); document.write( "If you need more help, or if you have any questions about the problem, feel free to email me at
jim_thompson5910@hotmail.com\n" ); document.write( " \n" ); document.write( "