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John F. Dumas

Python - Prime Factorization

► Problem Description: There are two kinds of numbers: composite and prime. A prime number has no factors other than 1 and itself. Composite numbers can be broken down into the product of 2 or more prime numbers.

Here are some examples:

 Number Prime Factorization Prime Or Composite 2 2 Prime 3 3 Prime 4 2 * 2 Composite 5 5 Prime 6 2 * 3 Composite 7 7 Prime 8 2 * 2 * 2 Composite 9 3 * 3 Composite 10 2 * 5 Composite

Note also that when the number is composite, the factors are shown in order from smallest to largest.

Write a program to generate the table above but instead of just showing the numbers from 2 to 10, show them all the way to 10,000. Below, under the Source Code section you can find the file 'output.txt' which shows the correct output for all numbers from 2 to 10,000.

► Example Output:

```   Number Prime Factorization                                Prime Or Composite
------ -------------------                                ------------------
2      2                                                  Prime
3      3                                                  Prime
4      2 * 2                                              Composite
5      5                                                  Prime
6      2 * 3                                              Composite
7      7                                                  Prime
8      2 * 2 * 2                                          Composite
...
9993   3 * 3331                                           Composite
9994   2 * 19 * 263                                       Composite
9995   5 * 1999                                           Composite
9996   2 * 2 * 3 * 7 * 7 * 17                             Composite
9997   13 * 769                                           Composite
9998   2 * 4999                                           Composite
9999   3 * 3 * 11 * 101                                   Composite
10000  2 * 2 * 2 * 2 * 5 * 5 * 5 * 5                      Composite
```

► Source Code

All files (zip file)

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