Latest Capgemini Aptitude Question SOLUTION: 9^n is divisible by 144!. then what is the value of n?

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9^n is divisible by 144!. then what is the value of n?

Asked In Capgemini Atasi (9 years ago)

Unsolved Read Solution (8)

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Read Solution (8) :

Keerthi  (9 years ago)

9 is 3*3=3^2..so,
144/3=48
48/3=16
16/3=5
5/3=1
add all qotients=48+16+5+1=70,,,,,70/2(70 divided by 2 because of 3 power 2 )=35
Answer is 35...

Is this solution Helpfull? Yes (27) | No   

RAJIV BAGHEL  (8 years ago)

answer is 35
process is like how we check number of zeroes in some n!
now 144!/9^n
break 9 into least prime
so now 144/3 + 144/9 + 144/27 + 144/81 ...
48 + 16 + 5 + 1 we take only integer value
now total is 70 but we checked for 3 so answer is 70/2 ; power factor of 3 is 2
so 35

Is this solution Helpfull? Yes (4) | No   

Arkja tiwari  (9 years ago)

1 to 100 there are 11 no. Which are divisible by 9 and 100 to 144..... there are total 5 no. So for complete divison total 16 9s are required...

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Abhishek singh  (9 years ago)

144/2=72
72/2=36
36/2=18
18/2=9
9/2=4
4/2=2
2/2=1
72+36+18+9+4+2+1=142

Is this solution Helpfull? Yes (1) | No (9)  

Deepak Kumar Sahu  (8 years ago)

wrong question.....144! is divisible by 9^35....9^35 is not divisible by 144!

Is this solution Helpfull? Yes (1) | No (5)  

kishore kumar pola  (6 years ago)

as i take ref from keerthi,arkja both the ans are write but some people may not understand how 70 is becoming 35
that is very simple 70 is for no of 3's in 144! but in question they asked no of 9's so half the no of 70 which is 35

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Vipul Pophale  (9 years ago)

Will ti possible? coz when we look for any power of 9 it will end with unit digit either 9 or 1 and 144! ends with unit digit 0

Is this solution Helpfull? Yes | No (9)  

ishani  (9 years ago)

I think answer is 35 !

Is this solution Helpfull? Yes | No (1)  

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