Latest Elitmus Aptitude Question SOLUTION: P is a no. which has exactly 3 factors which divide 25! Then whats is the greatest power of 3 in (p-25)!

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P is a no. which has exactly 3 factors which divide 25! Then whats is the greatest power of 3 in (p-25)!

Asked In Elitmus Sniper (7 years ago)

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rajat  (7 years ago)

suppose p=125 has three factor 125==5*5*5;
(125-25)=100;
power of 3=100/3=33.33/3+11.11/3+3.3/3=47+11+3+1=48

Is this solution Helpfull? Yes (6) | No (10)  

Mohd Azeem Saifi  (7 years ago)

Only perfect squares of prime numbers can have three factors, all other numbers will have even number of factors .

Hence factors of P are 1,p and p^2, where p is a prime number.

Since P divides 24!, the greatest value p can have is 11.( Since 11^2 is 121, which can be obtained from the terms 22 and 11 from 24!. If you try to take 13, a single 13 can be obtained but for a second 13, we need 26, which is clearly not available.)

Hence the number P is 121.

Therefore (P-25) is 96.

The highest power of 3 in (p-25)! is obtained by as follows:

[96/3]+[96/3^2]+[96/3^3]+[96/3^4]= 32+10+3+1=46

Hence the answer is 46.

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Devkaran Singh  (7 years ago)

p=125 has three factor 125==5*5*5;
(125-25)=100;

power of 3 = 100/3 + 33.33 /3 + 11.11 /3 + 3.3 /3
= 33 + 11 + 3 + 1 = 48

Is this solution Helpfull? Yes (1) | No (7)  

Manisha Choudhary  (7 years ago)

[100/3]+[100/3^2]+[100/3^3]+[100/3^4]= 33+11+3+1=48

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