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Algebra

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3 Mar 2008 19:43:38 IST

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How many positive integers less than 2008 have exactly seven factors (including 1 and the number itself)?

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sreeraman nagasubramaniyan

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Joined: 17 Jan 2008

Posts: 510

3 Mar 2008 20:37:10 IST

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suppose we have a number A

to find the number of factors we express it as powers of prime numbers

suppose a number is expresses as

2^x3^y then no of factors is (x+1) (y+1)

here (x+1)(y+1) = 7

so x+1 = 7 and y+1 = 1

=> x=6 ,y=0

x+1 = 1 and y+1 = 7

=> x=0,y=6

so now 2⁶ 3⁶ are less than 2008 but 5⁶ >2008

so there r just 2 numbers

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