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# An integer is the product of four prime numbers, two of

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Manager
Joined: 07 Jul 2005
Posts: 104

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An integer is the product of four prime numbers, two of [#permalink]

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25 Nov 2005, 17:47
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An integer is the product of four prime numbers, two of which are the same. How many factors does the integer have?

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Senior Manager
Joined: 05 Oct 2005
Posts: 485

Kudos [?]: 6 [0], given: 0

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25 Nov 2005, 18:13
12

3 prime factors, 1 of them in its second power

x^(2) , y^(1) , z^(1)

(2+1)*(1+1)*(1+1)

= 12

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SVP
Joined: 05 Apr 2005
Posts: 1708

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25 Nov 2005, 18:16
let a = 2
b=3
c=5
integer = a x a x b x c = 2x2x3x5=60
factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

altogather 12.

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Manager
Joined: 07 Jul 2005
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25 Nov 2005, 20:28
Hey YB: I am little lost. How did you come up with that formula? Can you tell me the steps please?

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SVP
Joined: 28 May 2005
Posts: 1700

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Location: Dhaka

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26 Nov 2005, 01:18
because we have 3 different prime nmuber

so factors shoud be 3! = 6

now the duplicate one will be repeated twice so total factors = 6*2 =12
_________________

hey ya......

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26 Nov 2005, 01:18
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