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# How many different positive integers are factors of 441? A)

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Intern
Joined: 30 May 2005
Posts: 18
How many different positive integers are factors of 441? A)  [#permalink]

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06 Jun 2007, 19:32
How many different positive integers are factors of 441?

A) 4
B) 6
C) 7
D) 9
E) 11

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Senior Manager
Joined: 24 Nov 2006
Posts: 331
Re: Number Properties Question 3  [#permalink]

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06 Jun 2007, 19:40
1
700dreamer wrote:
How many different positive integers are factors of 441?

A) 4
B) 6
C) 7
D) 9
E) 11

441 = 3^2*7^2. Number of factors = (2+1)*(2+1) = 9 => D.
CEO
Joined: 17 May 2007
Posts: 2866

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06 Jun 2007, 22:34
Hi andr359, could you please elaborate on how you deduced (2+1)*(2+1) ?

Seems like a good short cut to use after finding prime factors.
Manager
Joined: 17 Oct 2006
Posts: 52

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06 Jun 2007, 23:23
1
Let's say N=(a^x)*(b^y)*(c^z)
then the total number of factors including N are (x+1)(y+1)(z+1)
Lets say we have 84, so the prime factors are 2,2,3,7. So 84=2^2*3*7
so total factors of 84 including 84 are (2+1)(1+1)(1+1)=3*2*2=12 which are 1,2,3,4,6,7,12,14,21,28,42,84.
Take another example of 64
64=2^6 so factors are (6+1)=7 which are 1,2,4,8,16,32,64
I hope this helps
CEO
Joined: 17 May 2007
Posts: 2866

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06 Jun 2007, 23:56
Yup that definitely helps mate. What about the situation where there are more than 3 prime factors ? Say a number like 420 ?

FYI The nine factors for 441 are
1,441
3,147
7,63
9,49
21
I did it the hard way
Director
Joined: 03 Sep 2006
Posts: 803
Re: Number Properties Question 3  [#permalink]

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07 Jun 2007, 00:16
700dreamer wrote:
How many different positive integers are factors of 441?

A) 4
B) 6
C) 7
D) 9
E) 11

Factors of 441 are (3^2)*(7^2)

Therefore number of postive integer factors are (2+1)*(2+1) = 9

Manager
Joined: 17 Oct 2006
Posts: 52

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07 Jun 2007, 00:28
Dude the rule is the same. for 420 the prime factors are 2*2*3*5*7 therefore (2+1)(1+1)(1+1)(1+1)=24. The concept is that the more variety of prime factors, the more combinations can we have of them and therefore more factors.
(BTW, i tried to write down all the 24 factors for u but after 18 my brain stopped working )
bye
CEO
Joined: 17 May 2007
Posts: 2866

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07 Jun 2007, 00:35
Thanks mate, very useful stuff
Senior Manager
Joined: 22 Jun 2006
Posts: 277

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07 Jun 2007, 14:17
Very Cool Stuff
WOW =)
Non-Human User
Joined: 09 Sep 2013
Posts: 8508
Re: How many different positive integers are factors of 441? A)  [#permalink]

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15 Nov 2017, 21:12
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# How many different positive integers are factors of 441? A)

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