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?