Question

the number of zero in the product of the first 100 natural number. Answer is 24... please give solution...​

Answer 1

Answer:

24 zeroes.

Step-by-step explanation:

Zero basically comes when 10 is multiplied to a number, but 10 also arrives when there is product of 2 and 5.

So we need to find how many times 2 and 5 appear and club them to get 10.

Since there will be too many 2's are available in the multiplication so we have it more than enough so we can just find how many 5's in the product of all numbers.

Now 5 appears only one time in the numbers : 5,10,15,20,30,35,40,45,55,60,65,70,

80,85,90,95

In the above 16 numbers we are getting just one 5 each time when we factorise each number.

[35 = 5*7. 80 = 5*2*2*2*2]

But in 4 numbers 25,50,75,100 we get 5 two times when we factorise each number.

[75 = 5*5*3]

So number of 5's in these four numbers is = 2*4 = 8

Hence, total numbers of zeroes must be

16 + 8 = 24

{Since we will have 24 5's and 24 2's available to make it 10}.

Hope it helps

HAKUNA MATATA :))