prime (pr ̄im) n. [ME, fr. MF, fem. of prin first, L primus; akin to L prior] 1: first in time: original 2 a: having no factor except itself and one ⟨3 is a ∼ number⟩ b : having no common factor except one ⟨12 and 25 are relatively ∼⟩ 3 a: first in rank, authority or significance: principal b: having the highest quality or value ⟨∼ television time ⟩ [from Webster’s New Collegiate Dictionary] The most relevant definition for this problem is 2a: An integer g > 1 is said to be prime if and only if its only positive divisors are itself and one (otherwise it is said to be composite). For example, the number 21 is composite; the number 23 is prime. Note that the decompositon of a positive number g into its prime factors, i.e., g = f1 × f2 × · · · × fn isuniqueifweassertthatfi >1foralliandfi ≤fj fori<j. One interesting class of prime numbers are the so-called Mersenne primes which are of the form 2p − 1. Euler proved that 231 − 1 is prime in 1772 — all without the aid of a computer. Input The input will consist of a sequence of numbers. Each line of input will contain one number g in the range −231 < g < 231, but different of -1 and 1. The end of input will be indicated by an input line having a value of zero. Output For each line of input, your program should print a line of output consisting of the input number and itsprimefactors. Foraninputnumberg>0,g=f1×f2×···×fn,whereeachfi isaprimenumber greater than unity (with fi ≤ fj for i < j), the format of the output line should be g=f1 xf2 x... xfn When g < 0, if | g |= f1 × f2 × · · · × fn, the format of the output line should be g=-1xf1 xf2 x... xfn Sample Input -190 -191 -192 -193 -194 195 196 197 198 199 200 0
583 – Prime Factors 2/2 Sample Output -190 = -1 x 2 x 5 x 19 -191 = -1 x 191 -192 = -1 x 2 x 2 x 2 x 2 x 2 x 2 x 3 -193 = -1 x 193 -194 = -1 x 2 x 97 195 = 3 x 5 x 13 196 = 2 x 2 x 7 x 7 197 = 197 198 = 2 x 3 x 3 x 11 199 = 199 200 = 2 x 2 x 2 x 5 x 5