Let for all n , natural numbers f(n) = product of non zero digits of n.find the largest prime divisor of


f(1) + f(2) + ...... + f(999).                                                         (the answer is 103)

2 years ago

Share

Answers : (5)

                                        

The question is the largest prime no that divides f(n)


Lets simplify f(1)+f(2)+f(3)+f(4)+...+f(999)


= (1+2+3+4...+9)+1+(1+2+3+4+...+9)+2+2(1+2+3+4+...+9) +3+3(1+2+3+4+...+9) +...


On simpifying and using formula for summation of n natural no n(n+1)/2we get that the summation is 


Full solution is not given as u needed hints fr the question


((9*10)/2+1)((9*10)/2+1)((9*10)/2+1) -1 = (46*46*46)-1  97335


On prime factorization os 97335 we getthe last prime as 103 and hence we said tht the largest prime tht devides

2 years ago
                                        

Thnks for ur reply


 


But,what does 

product of non zero digits of n  



mean?


2 years ago
                                        

The product of non zero digits of n is like  f(999) = 9*9*9 , f(998)= 9*9*8, f(101)= 1*1 (0 not included)

2 years ago
                                        

How did u do this?


 f(1)+f(2)+f(3)+f(4)+...+f(999)= (1+2+3+4...+9)+1+(1+2+3+4+...+9)+2+2(1+2+3+4+...+9) +3+3(1+2+3+4+...+9) +...

2 years ago
                                        

This can be done in following way


This can be done in f(1)= 1, f(2)=2, ... ,f(9)=9 , f(10) = 1 , f(11) =(1*1), f(12)= (1*2), f(13)=(1*3),...f(19),f(20)= 2 , f(21)= (2*1) and so on

2 years ago

Post Your Answer

More Questions On Algebra

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
if f(x)=x^4+x^3-2x^2-8x then which of the following are true?(a)f(x)=0 has 2 real roots . (b)f(x)=0 has real roots in (-1,2) sum of real roots of f(x)=0 is 2 (d) product of real roots isof...
 
 
Hello student, Please find the answer to your question below Iam unable to interpret your query.i think some part of the question is missing here because check whether constant term is...
  img
SHAIK AASIF AHAMED one month ago
 
Is there any constant term in the given polynomial? If there is no constant, then one of the roots will be ‘0’ and the other root is ‘2’. Other roots are complex. No. of real roots = 2 Sum...
 
Y RAJYALAKSHMI 3 months ago
Find the real values of the parameter ‘a’ for which atleast one complex number z =x+iy satisfies both the equality |z-ai|=a+4 and the inequality |z-2| is less than 1 .
 
 
Ans: Hello Student, Please find the answer to your question below For having atleast one solution for both the equation, the first circle should intersect with 2 nd circle on the x –...
  img
Jitender Singh 3 months ago
 
first of all is not right as given in qus this is less than 1 not equal second thing this qus is from resonannce assignment and ans is (-21/10 ,- 5/6)
 
saurabh 2 months ago
if x be real number such that x^3+4x=8 then value of x^7+64x^2=?
 
 
Hello student, Please find the answer to your question below (x^3 + 4x)^2 = 8^2 => x^6 + 16x^2 + 8x^4 = 64; Multiply both sides by x => x^7 + 16x^3 + 8x^5 = 64x; Add 16x^3 in both...
  img
SHAIK AASIF AHAMED 2 months ago
evaluate the following integral ∫ e^(3x) / e^(3x) + 1 dx
 
 
Ans: Hello student, Please find the answer to your question below
  img
Jitender Singh one month ago
Integrate cosecx.sec3x
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 3 months ago
View all Questions »