Latest TCS Aptitude Question SOLUTION: Find the no of zeros in the product of 1^1*2^2*3^3*.....*49^49??

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Find the no of zeros in the product of 1^1*2^2*3^3*.....*49^49??

Asked In TCS Raj (11 years ago)

Solved Aman Read Solution (8)

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Read Solution (8) :

Aman  (11 years ago)

consider the case of multiples of 5

5^5 x 10^10 x 15^15 x 20^20 x 25^25 x 30^30 x 35^35 x 40^40 x 45^45
or
5^5 x 10^10 x 15^15 x 20^20 x (5^2)^25 x 30^30 x 35^35 x 40^40 x 45^45
or
5^5 x 10^10 x 15^15 x 20^20 x 5^50 x 30^30 x 35^35 x 40^40 x 45^45

total zeros at the end of product 5^5 x 10^10 x 15^15 x 20^20 x 25^25 x 30^30 x 35^35 x 40^40 x 45^45 will be 5+10+15+20+50+30+35+40+45 = 250 zeros

Is this solution Helpfull? Yes (79) | No (17)  

joy dey  (11 years ago)

2*5=10
5^5 5 times 5
10^10 10 times 5
15^15 15
......
25^25 50
.....
5+10+15+20+2*25+30+35+40+45=250

Is this solution Helpfull? Yes (12) | No (4)  

SHANU MAHAJAN  (11 years ago)

can u explain me the logic behind taking multiples of 5. 5^5 do not contain single 0

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

shekhar pankaj  (11 years ago)

same as of aman but
5+10+15.......+45

gives sum 225

Is this solution Helpfull? Yes (7) | No (9)  

Srinivas Rao  (9 years ago)

Normally to count number of zeroes we need no of 5x2 pairs
As the pair 5x2=10 generate a zero.
In this case more number of 2's than 5.
So it would b sufficient to count no of 5,s
5^5 x 10^10 x 15^15 x 20^20 x 25^25 x 30^30 x 35^35 x 40^40 x 45^45
IN 25^25 WE GET 50 5'S AS 25=5*5
COUNT TOTAL OCCURENCES OF 5
5+10+15+20+50+30+35+40+45= 250 ZEROES

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Jagadeesh  (11 years ago)

10^2*20^2*30^2*40^2
Then we get the number of zeros as = 8
i.e eight zeros.

Is this solution Helpfull? Yes (3) | No (48)  

Haritha   (9 years ago)

Can u explain clearly

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Arun kumar prajapati  (9 years ago)

No. Of zeros = no. Of 5
So just count how many 5s are .

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