数学题求救.LetE(x)denotethesumoftheexponentsintheprimefactorizationoftheintegerx.Forexample,E(60)=4,because60=22×31×51and22+11+11=4.whichofthefollowingintegersisE(x)>andwhy? 207 300

Question

数学题求救.
Let E(x) denote the sum of the exponents in the prime factorization of the integer x.For example,E(60) = 4,because 60 = 22 × 31 × 51 and 22 + 11 + 11 = 4.which of the following integers is E(x) >
and why?

207
 300
 384
 
400
 
625
I would like to know why.thx
make a little correction.2^x3^x5^ and 2+1+1=4
^ which means the index 2,1,1.
sorry,coz i barely know how to type the math symbol on internet.

Answer 1

factorization of 207=3^1*3^1*23^1 ,so E(207)=1+1+1=3
factorization of 300=2^2*3^1*5^2 ,so E(300)=2+1+2=5
factorization of 384=2^7*3^1 ,so E(384)=7+1=8 > 7
factorization of 400=2^4*5^2,so E(400)=4 +2=6
factorization of 625=5^4 ,so E(625)=4