What will be the power of 10 in the product 1*2*3*4*5......*40

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09 Dec 2011 powers

What will be the power of 10 in the product 1*2*3*4*5......*40

OPtion

1) 1
2) 2
3) 3
4) 4
5) 5
6) 6
7) 7
8) 8
9) 9
10) none of these

Solution

10 = 5*2, so we should consider either the number of 5 or number of 2, whichever is less,
Total no of fives = 8+1 = 9

Correct Option: 9 Best Solution (9)

Dr.Dipin Singh   12 years AGO

the power of 10 in the product 1*2*3*4*5......*40 = quotient of 40/5 + quotient of 40/25 = 8+1 = 9 .. option 9

Like? Yes (5) | No (2)  

chhagan mathuriya   12 years AGO

10 comes by multiplication of 5 and 2.

S if we calculate number of factors of 5 which is equal to trailing zeros or powers of 10.

40/5=8

8/5= 1

so 8+1=9 is the answer.

Like? Yes (3) | No   

Shubham   12 years AGO

no of 5's i.e. 9.

Like? Yes (2) | No (1)  

Honey Goel   12 years AGO

10,20,30,40
5x2,15x2,25x4,35x2

Like? Yes (2) | No (1)  

Vivek Yadav   12 years AGO

40/5=8
8/5=1
1/5=0
so add 0+1+8=9.
answer will be 9.

Like? Yes (1) | No   

Raja m   12 years AGO

The power is 10 depends on 2 & 5. Since 5 more infrequently and occurs only 9 times, the power of 10 is also 9.

Like? Yes (1) | No   

bhargav   12 years AGO

40/5 + 8/5 +1/5= 9 only modulus

Like? Yes (2) | No (1)  

Rohit kumar   12 years AGO

the number of zero in n factorial is given by:- n/5+n/5^2+..... so on...... leave the fractional part......
so considering this :- it will be 40/5 +40/25 + 40/125 =8 +1 =9

Like? Yes (2) | No (1)  

catrocker   12 years AGO

basically we have to check the combination of 2 and 5 because 2*5 makes 10.....

so only 9 combinations are possible in this scenario....
so my take is 9....

Like? Yes (1) | No