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# How many zeros does 250! end with?

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Director
Joined: 11 Feb 2015
Posts: 615
How many zeros does 250! end with?  [#permalink]

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03 Jul 2018, 03:04
00:00

Difficulty:

15% (low)

Question Stats:

86% (01:08) correct 14% (01:37) wrong based on 32 sessions

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How many zeros does 250! end with?

A. 60
B. 62
C. 64
D. 68
E. 70

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Manish

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Joined: 02 Aug 2009
Posts: 7106
Re: How many zeros does 250! end with?  [#permalink]

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03 Jul 2018, 04:33
CAMANISHPARMAR wrote:
How many zeros does 250! end with?

A. 60
B. 62
C. 64
D. 68
E. 70

Numerous question on the subject..
ans wr would depend on the number of times 5 comes in 1*2*3*...*250

it is $$\frac{250}{5}+\frac{250}{5^2}+\frac{250}{5^3}=50+10+2=62$$
beyond 250/5^3 it will become<1, so discard

B
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: How many zeros does 250! end with?  [#permalink]

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03 Jul 2018, 04:43
1
To calculate zeros in any n! we have to check how many "5" it has

250/5=50
250/5^2=10
250/5^3=2

50+10+2=62

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Re: How many zeros does 250! end with?  [#permalink]

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03 Jul 2018, 07:28
CAMANISHPARMAR wrote:
How many zeros does 250! end with?

A. 60
B. 62
C. 64
D. 68
E. 70

$$\frac{250}{5} = 50$$
$$\frac{50}{5} = 10$$
$$\frac{10}{5} = 2$$

So, 250! must end in 62 zeroes, answer must be (B)
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Re: How many zeros does 250! end with? &nbs [#permalink] 03 Jul 2018, 07:28
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