Algebra Demystified 2nd Ed

Appendix FACTORING WITH PRIME NUMBERS 473

DeMYSTiFieD / Algebra DeMYSTiFieD / Gibilisco / 000-0 / Appendix

The first sixteen prime numbers

Prime Number Square of the Prime Number

2 4

3 9

5 25

7 49

11 121

13 169

17 289

19 361

23 529

29 841

31 961

37 1369

41 1681

43 1849

47 2209

53 2809

8. 1595 = 5 · 11 · 29


9. 1287 = 3 · 3 · 11 · 13


10. 540 = 2 · 2 · 3 · 3 · 3 · 5

What happens if we need to factor a number such as 3185? Do we really
need all the primes up to 59? Maybe not. We try the smaller primes first. More
than likely, one of them will divide the large number. Because 3185 ends in 5,
it is divisible by 5: 3185 ÷ 5 = 637. Now all that remains is to find the prime
factors of 637, so the list of prime numbers to check stops at 23. The reason
this trick works is that the prime factors of 3185 = 5 ∙ 673 are factors of 5 and

673. Once we divide the large number, the list of prime numbers to check is
     usually smaller.