Use Fermat Factorization to work out this factorization!
Note that 115 < √13431 < 116.
Select the squared value of a number, say 116. Then:
116² - 13431 = 25
Since 25 is the perfect square number, 116 works. Now, using this form:
n = s² - t² = (s - t)(s + t) where t is the value of the square root of some perfect square
We obtain:
13431 = (116 - 5)(116 + 5)
= 111(121)
Now, this should look obvious. Factor out each term by term to get:
111 x 121
= 3 x 37 x 11² or 3 x 11² x 37
So there are some numbers that are divisible by 13431. They are:
- 3
- 11
- 37
- 121
- 111
- 1221
- 4477
- 407
Note: Fermat Factorization only applies to factorizable odd number!