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# value of n - ps

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value of n - ps [#permalink]

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11 Jun 2007, 13:13
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if n is a positive integer and the product of all the integers from 1 to n, inclusive is a multiple of 990, what is the least possible value of n?

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11 Jun 2007, 15:05
if n is a positive integer and the product of all the integers from 1 to n, inclusive is a multiple of 990, what is the least possible value of n?
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You know that n>=1
Setting up the equation: 1*2*3*4*5*...*n = 990*integer
We also know that: 990 = 2*3*3*5*11

Therefore:
=> integer = (1*2*3*4*5*...*n) / (2*3*3*5*11)

If you eliminate some terms, we know that n must be 11 to make the division result an integer.

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11 Jun 2007, 17:12
990
= 99*10
= 3*11*2*5

The multiplying factor is probably 4*6*7*8*9*10

Smallest value of n is 11
11 Jun 2007, 17:12
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