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# The largest number amongst the following that will perfectly

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CEO
Joined: 15 Aug 2003
Posts: 3454
Followers: 67

Kudos [?]: 874 [0], given: 781

The largest number amongst the following that will perfectly [#permalink]

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29 Sep 2003, 21:10
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The largest number amongst the following that will perfectly divide 101^100 - 1 is

(1) 100 (2) 10,000 (3) 100100 (4) 100,000

Last edited by Praetorian on 29 Sep 2003, 21:45, edited 1 time in total.
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 13 [0], given: 0

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30 Sep 2003, 06:20
100?

preat: Do you know of a good trick to get the answer? Or does the source of this problem explain one? I used simple logic, as in, multiple of 101 can't have more than two zero's until it hits 100 power because the '1' in 101 won't let it happen. And that's how I got the answer. In actuality the answer could be 1000 but that's among the choices here.
Senior Manager
Joined: 22 Aug 2003
Posts: 257
Location: Bangalore
Followers: 1

Kudos [?]: 13 [0], given: 0

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30 Sep 2003, 09:04
101^100 -1 = (1 + 100)^100 -1
= 100C0*1 + 100C1*100 + ... + 100C100*(100)^100 -1
{writing binomial terms of (1+x)^n}

Thus divisible by 100*100 =10000
-vicky
30 Sep 2003, 09:04
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