Q1. Find the Highest power of 2 in 1! + 2! + 3! + .......+ 600!

Q2. what max. value of n in 160^n divides 100!.
A). 19 B). 24 C).26 D). 28

Q3. What is the number of consecutive zeros in the end of 1000! ?
A). 248 B). 249 C). 250 D). 251

• Q3. ans> no of consecutive 0 is 249
  1000/5=200
  200/5=40
  40/5=8
  8/5=1
  so, total no of consecutive 0 is (200+40+8+1)=249
• 10 years agoHelpfull: Yes(40) No(0)
• ans for qestion 2:
  160= 2^5*5
  100/2=50/2=25/2=12/2=6/2=3/2=1.....so 50+25+12+6+3+1=97/5=19
  whereas 100/5=20/5=4.......so 20+4=24 which is more than 19. so correct ans is 19.
  
• 10 years agoHelpfull: Yes(23) No(3)
• (1)
  highest power of 2 is 0..because everytime we take the sum it would be an odd number.
  for eg
  1!+2!+...+5!=155
  1!+2!+......+6!=875
  
• 10 years agoHelpfull: Yes(14) No(1)
• 1.We now, odd+even = odd. Since 1! is odd so the highest power of 2 is zero
  
  2 & 3. Highest power of n in N! is [N/n]+[N/n^2]+.......
  
  
• 10 years agoHelpfull: Yes(6) No(1)
• (2) Ans:- 160 prime factor is 2 and 5,but for 160 we need five 2's and one 5, check for no of 5 in 100!, using Highest power of n in N! is [N/n]+[N/n^2]+.... So we get 24 as answer. Now checking for 2 we get 97 using same formula. But we need pair of five 2's. So 97/5 gives 19 pair of five 2's which is less than 24 no. of 5. So 19 answer.
• 10 years agoHelpfull: Yes(6) No(0)
• ANS 1)596
  2)24
  3)249
• 10 years agoHelpfull: Yes(5) No(3)
• Q.3. number of zeros in 1000!=[1000/5]+[1000/25]+[1000/125]+[1000/625]=249
  Where [x] is x is nearest integer.
• 10 years agoHelpfull: Yes(4) No(0)
• 1000/5=200
  200/5=40
  40/5=8
  8/5=1
  200+40+8+1=249
• 10 years agoHelpfull: Yes(3) No(1)
• 1)1! will add 1 to sum nd thus altimately sum is odd n so odd no is not divisible by 2 so ans is 0
  
  2) 160= 2^5*5
  100/2+100/4+100/8+100/16+ 100/32+100/64=97
  that is it contain 2^97 i.e (2^5)^19
  100/5+100/25 =24
  total 19 2^5*5 combination
  so ans is 19
  
  3). 1000!/5 + 1000!/25 + 1000!/125 + 1000!/625= 249
  
• 10 years agoHelpfull: Yes(2) No(0)
• Q3
  1000/5=200
  1000/5*5=40
  1000/5*5*5=8
  1000/625=1
  bcz 1000
• 10 years agoHelpfull: Yes(1) No(1)
• q3. 1000!/5 + 1000!/25 + 1000!/125 + 1000!/625= 249
• 10 years agoHelpfull: Yes(1) No(0)
• Q1)answer is 9..as 512! is the max. no
• 10 years agoHelpfull: Yes(0) No(0)
• 1) highest power iz 9
  2) 24
  3) 248
• 10 years agoHelpfull: Yes(0) No(1)