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
A= 1 101 +2 101 +3 101 + 4 101 +......+34 101 . Find the remainder when A is divided by 70.
 
 
Hi, This question can be easily solved by using binomial theorem. Write 1 as 7-6 two as 7-5 and so on, remember that 7 multiple will be 7 and 8 will be written as 7+1 and so on. Now when you...
  img
Yash Baheti one month ago
if a,b,c,d,e,f,g,h,i are 9 different natural numbers then how many 3x3 and 2x2 matrices are formed with these numbers?
 
 
A 3x3 matrix will have 9 vacant places for the numbers to be put in from the available options i.e. 9 given numbers. So Number of arrangements of 9 numbers at 9 different places =...
  img
Ravi one month ago
log 3/4 log 8 (x 2 +7) + log 1/4 (x 2 +7) -1 = -2 Solve for x.
 
 
First reduce the eqn from double log to a single log eqn. Follow the steps: Remove the logbase3/4 using the exponential equivalent. This would give an eqn of 2 terms equated to a number...
  img
Ravi one month ago
evaluate the following integral ∫ (2 cos 2x + sec^2 (x)) / sin 2x + tan x – 5 dx
 
 
Ans: Hello student, Please find the answer to your question below
  img
Jitender Singh 3 months ago
Find the area bounded bythe curve y=cox,line joining [-pi/4,cos(-pi/4)] and [0,2],the line joining [pi/4,cos(pi/4)] and [0,2] . i have doubt on my answer which is almost 0[my answer]
 
 
Please check your answer then. Applying the property of even function here will be helpful. That could be a case I can expect that you have integrated the whole area in one integrand which...
  img
Ravi one month ago
find the solutions sin2x-12(sinx-cosx)+12=0
 
 
Ans: We need to do hit & trial in this case So the combined solution is This satisfy the original equation.
  img
Jitender Singh 5 months ago
View all Questions »