Question

Use Fermat's Factorization method to factor 2401. Show all of your work.

Answer 1

Fermat’s Factorization method is based on the representation of an odd integer as the difference of two squares.

For an integer n, we want a and b such as:

n = a^2 - b^2 = (a+b)(a-b) where (a+b) and (a-b) are the factors of the number n.

For the value 2401,

n = 2401

the first try for a is ceil value of square root of 2401, which is 49. Then, b^2 = 49^2 - 2401 = 0, as it is a perfect square. So, b = 0. So the factors of 2401 are:

(a - b) = 49-0 = 49 & (a + b) = 49+0 =49 i.e. (49,49) are the factors of the number 2401.

Thank you!