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# How many factors does 36^2 have? 2 8 24 25 26

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How many factors does 36^2 have? 2 8 24 25 26 [#permalink]

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14 Jun 2008, 17:06
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How many factors does 36^2 have?
2
8
24
25
26

Last edited by lionheart187 on 14 Jun 2008, 17:35, edited 1 time in total.
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14 Jun 2008, 17:27
I might be a little rusty here... but, here is what I think...

362 = 2 x 181 = I cant seem to break it down any furthur

So, A

"Ooops I completely overlooked the "^".... lesson learnt"

Last edited by Kalyan on 14 Jun 2008, 21:18, edited 1 time in total.
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14 Jun 2008, 17:38
are u sure its not 36??
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14 Jun 2008, 20:55
lionheart187 wrote:
How many factors does 36^2 have?
2
8
24
25
26

36^2=6^4

6^4=(3*2)^4

the factors have to be (4+1)(4+1)=25
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15 Jun 2008, 21:19
fresinha12 wrote:
lionheart187 wrote:
How many factors does 36^2 have?
2
8
24
25
26

36^2=6^4

6^4=(3*2)^4

the factors have to be (4+1)(4+1)=25

Could you explain how you got 4 + 1 freshina?
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15 Jun 2008, 22:49
lionheart187 wrote:
fresinha12 wrote:
lionheart187 wrote:
How many factors does 36^2 have?
2
8
24
25
26

36^2=6^4

6^4=(3*2)^4

the factors have to be (4+1)(4+1)=25

Could you explain how you got 4 + 1 freshina?

this is a property of integers

if an integer can be broken down into its prime factors $$m^x*n^y$$ ... eg $$2^4*3^4$$as in this case, the number of factors of that integer can be determined by (x+1)(y+1)...

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15 Jun 2008, 23:03
lionheart187 wrote:
fresinha12 wrote:
lionheart187 wrote:
How many factors does 36^2 have?
2
8
24
25
26

36^2 = 6^4
6^4 = (3*2)^4

the factors have to be (4+1)(4+1)=25

Could you explain how you got 4 + 1 freshina?

this is a formula for finding no of factors in such wired questions. How do you find factors of 5000^2? remember theis formula and use it.

1000^2 = (2x2x2x5x5x5)^2 = (2x5)^6

so the number of factors = (6+1)(6+1) = 49
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17 Jun 2008, 08:35
lionheart187 wrote:

this is a formula for finding no of factors in such wired questions. How do you find factors of 5000^2? remember theis formula and use it.

1000^2 = (2x2x2x5x5x5)^2 = (2x5)^6

so the number of factors = (6+1)(6+1) = 49

Quick question. Why did you just find the number of factors for 1000^2 as oppossed to 5000^2 (in the original question)? Wouldn't you be missing an extra "5" thus making the number of factors = 63? -->

5000^2 = (2x2x2x5x5x5x5)^2 = (2)^6 * (5)^8

so the number of factors = (6+1)(8+1) = 63
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Factorials were someone's attempt to make math look exciting!!!

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17 Jun 2008, 08:47
Broker,

its a typo. Tiger mistyped 5000^2 in the original question. His solution is correct for 1000^2.
your solution is correct for 5000^2
Re: MGMAT Prob   [#permalink] 17 Jun 2008, 08:47
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