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# Find the number of zeroes at the end of the products

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Director
Joined: 26 Feb 2006
Posts: 905
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Find the number of zeroes at the end of the products [#permalink]  12 Jul 2007, 23:08
00:00

Difficulty:

(N/A)

Question Stats:

100% (01:16) correct 0% (00:00) wrong based on 1 sessions
Find the number of zeroes at the end of the products 12*18*15*40*25*16*55*105

(a)10
(b) 20
(c) 8
(d) 12
(e) 6
Senior Manager
Joined: 04 Jun 2007
Posts: 348
Followers: 1

Kudos [?]: 15 [0], given: 0

Re: PS: Zeros [#permalink]  12 Jul 2007, 23:42
Himalayan wrote:
Find the number of zeros at the end of the products 12*18*15*40*25*16*55*105

(a)10
(b) 20
(c) 8
(d) 12
(e) 6

The number of zeros will depend on the number of 10s in the product, or the number of (2*5)s.

12*18*15*40*25*16*55*105 can be broken up into number of 2s and 5s as

2^2, 2, 5, 2^3 * 5, 5^2, 2^4, 5, 5.

There are 10 2s and 6 5s. Hence, number of trailing zeros will be 6. (E)
Director
Joined: 09 Aug 2006
Posts: 766
Followers: 1

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Re: PS: Zeros [#permalink]  12 Jul 2007, 23:45
Himalayan wrote:
Find the number of zeroes at the end of the products 12*18*15*40*25*16*55*105

(a)10
(b) 20
(c) 8
(d) 12
(e) 6

Just look at the units digit of each product:
12*18 --> units digit = 6
6*15 --> units digit = 0
0*40 --> units digit = 0
0*25 --> units digit = 0
0*16 --> units digit = 0
0*55 --> units digit = 0
0*105 --> units digit = 0

Total number of 0's=6
Re: PS: Zeros   [#permalink] 12 Jul 2007, 23:45
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