Is the question correct??
because 500 is also factor or 50!..
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Factors
Source: Beat The GMAT — Problem Solving |
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Cans!!
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Cans!!
The question basically asks you to find how many zeros 50! has.
To find the No of zeros,
5 | 50
5 | 10 - 0
5 | 2 - 0
So, its 10+2 = 12 zeros.
So 10^12 will be a factor of 50!
To find the No of zeros,
5 | 50
5 | 10 - 0
5 | 2 - 0
So, its 10+2 = 12 zeros.
So 10^12 will be a factor of 50!
Rephrased, the question is asking the number of times 10 appears in the factorisation of 50!
The number 10 will appear when 5 is multiplied by 2 or when there is a number that is a multiple of 10.
Between 1 to 10 inclusive
We have 1,2,3,4,5,6,7,8,9,10
so 10^2
Between 11 to 20 inclusive
we have 11 12 13 14 15 16 17 18 19 20
We have a 5 and 20 which can be rewritten as 5*3 and 2*10 so from these two we have10^2
Between 21 to 30 inclusive
We have 21 22 23 24 25 26 27 28 29 30
From 25 we have 5*5 and two 2s can be taken from 24 or any other even# in this set to make 10^2
And we have 30 which is 3*10
So we have 10^3
Between 31 to 40 inclusive
We have 31 32 33 34 35 36 37 38 39 40
From 35 we have one 5 and from 40 we have 4*10. So to 5 we multiply the 2 from any other even# in the set to get 5*2. So in this set we have 10^2
Between 41 to 50 inclusive
we have 41 42 43 44 45 46 47 48 49 50
From 45 we have 9*5 and from 50 we have 5*10. So that is two 5s and one 10. So in this set we can borrow two 2s from any other even number to get 10^3
So in this set we have 10^3
Multiplying all of them together we have 10^3*10^2*10^3*10^2*10^2=[spoiler]10^12[/spoiler] Hence B
The number 10 will appear when 5 is multiplied by 2 or when there is a number that is a multiple of 10.
Between 1 to 10 inclusive
We have 1,2,3,4,5,6,7,8,9,10
so 10^2
Between 11 to 20 inclusive
we have 11 12 13 14 15 16 17 18 19 20
We have a 5 and 20 which can be rewritten as 5*3 and 2*10 so from these two we have10^2
Between 21 to 30 inclusive
We have 21 22 23 24 25 26 27 28 29 30
From 25 we have 5*5 and two 2s can be taken from 24 or any other even# in this set to make 10^2
And we have 30 which is 3*10
So we have 10^3
Between 31 to 40 inclusive
We have 31 32 33 34 35 36 37 38 39 40
From 35 we have one 5 and from 40 we have 4*10. So to 5 we multiply the 2 from any other even# in the set to get 5*2. So in this set we have 10^2
Between 41 to 50 inclusive
we have 41 42 43 44 45 46 47 48 49 50
From 45 we have 9*5 and from 50 we have 5*10. So that is two 5s and one 10. So in this set we can borrow two 2s from any other even number to get 10^3
So in this set we have 10^3
Multiplying all of them together we have 10^3*10^2*10^3*10^2*10^2=[spoiler]10^12[/spoiler] Hence B
