Latest TCS Aptitude Question SOLUTION: what is the highest power of 15 which will divide 90! exactly?

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what is the highest power of 15 which will divide 90! exactly?

Asked In TCS vinodhini (8 years ago)

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Arpan Chakrabarty  (8 years ago)

ans is : 21
15=5*3
take factors of 5 & 3 (like: 5 , 25 , 125 ... )

then , (90/5 + 90/25 ) [ 125 can not be taken as it is grater than 90 ]
= (18+3)
= 21
same as for 3 , (90/3 + ..... +90/81) = 44

so, take lowest one
ans is 21

Is this solution Helpfull? Yes (20) | No (3)  

pallavi kumari  (8 years ago)

Ans is 6.
90! contains 6 factors of 15.
1.......15...30....45...60...75...90
Thus highest power required is 6

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Ajay kumar  (8 years ago)

since 15=5*3
so to divide 90 completelyby 15 we will divide by 5&3 and calculate max powers
so in this case power of 3 will be excluded because value of higher term will be considered as power 3 will be more than power of 5and we will have to take common powers . so 90/5=18 here we take only quotient ,18/5=3
so answer will be max power of 15=18+3=21ans

Is this solution Helpfull? Yes (7) | No (2)  

Alok pratap singh  (8 years ago)

Ans is 21
15=3*5
3 will be more than 5 so wecalculate max power of 5 as we get 15 after multiplying 3 and 5.
power of 5 in 90!=90/5+90/5*5=21

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jayalakshmi  (7 years ago)

15 co primes are 3*5
to find the highest power of 3 divides 90!
[90/3]=30
[30/3]=10
[10/3]=3
[3/3]=1
[1/3]=0

take the sum=44

now highest power of 5 divides 90! exactly

[90/5]=18
[18/5]=3
[3/5]=0

sum=18+3=21

min(44,21)=21

ans is 21

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Shankar kumar  (8 years ago)

n=10 for exactly divided by 90

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PRIYA AGARWAL  (8 years ago)

21 as 15=3*5
and the highest power of 5 in 90! is 21 and the highest power of 3 in 90! is 44. so together 3 and 5 as 15 will be the power of 21

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zebul zareef  (8 years ago)

no any power of 15 will be divide by 90

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lalit  (8 years ago)

correct answer is 40.

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NIVETHA  (8 years ago)

IN 15 is written as 5*3.so we are taking the value of the lcm method and the top method has been cancel add the next value for seperate 5 and 3
answer will be 21

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