Factoring 1001 by Hand: A Simple Guide

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Homework Statement


Is there any simple way to factor 1001=7*11*13 by hand?


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The Attempt at a Solution

 
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Since last digit in 1001 is one it can be divided by either 1 or 3 or 7 or 9.Try one by one. You can see that 7 is a factor. Proceed in the same manner.
 
How do you know that a priori? Why does it need to be less than 10?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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