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# How many factors does 36^2 have?

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Current Student
Joined: 29 Jan 2005
Posts: 5218
How many factors does 36^2 have? [#permalink]

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13 Nov 2006, 07:58
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How many factors does 36^2 have?

A. 2
B. 8
C. 24
D. 25
E. 26

OPEN DISCUSSION OF THIS QUESTION IS HERE: how-many-factors-does-36-2-have-126422.html
[Reveal] Spoiler: OA
Senior Manager
Joined: 24 Oct 2006
Posts: 339

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13 Nov 2006, 08:15
1
KUDOS
Learnt this somewhere in this forum.

36^2=2^4*3^4

Take the powers of each prime factor, add 1 and multiply.

5*5=25 factors
Senior Manager
Joined: 17 Oct 2006
Posts: 433

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08 Dec 2006, 09:14
How many factors does 36^2 have

A)2
B)8
C)24
D)25
E)26

Plz explain ur method. thanks!
Senior Manager
Joined: 19 Jul 2006
Posts: 358

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08 Dec 2006, 11:46
36^2 = 2^4 * 3^4

number of factors = ( 4+1) * (4+1) = 25
SVP
Joined: 08 Nov 2006
Posts: 1554
Location: Ann Arbor
Schools: Ross '10

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08 Dec 2006, 12:22
AK, can you please explain the logic you used. I dont get it.
Senior Manager
Joined: 19 Jul 2006
Posts: 358

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08 Dec 2006, 12:46
AK, can you please explain the logic you used. I dont get it.

express number ( say N) as products of its prime factors ( say a,b,c)

N = a ^ p + b ^ q + c ^ r

Now number of factors of given number N = ( p +1) * (q+1)* (r+1)
Director
Joined: 28 Dec 2005
Posts: 919

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08 Dec 2006, 14:20
Ak I did not know this. Thank you! Did you mean:

N = a ^ p * b ^ q * c ^ r
Senior Manager
Joined: 17 Oct 2006
Posts: 433

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08 Dec 2006, 15:26
AK wrote:
AK, can you please explain the logic you used. I dont get it.

express number ( say N) as products of its prime factors ( say a,b,c)

N = a ^ p + b ^ q + c ^ r

Now number of factors of given number N = ( p +1) * (q+1)* (r+1)

Thanks for this formula. I assume u meant multiplication above rathar than addition.
Director
Joined: 01 May 2007
Posts: 793

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10 May 2008, 19:05
How many factors does 36^2 have?
2
8
24
25
26
Director
Joined: 01 May 2007
Posts: 793

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10 May 2008, 19:39
That is correct, but how did you get 25?
Director
Joined: 23 Sep 2007
Posts: 782

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10 May 2008, 19:42
the short cut for this type of question is to factor the original number to prime numbers

36^2 = 2^4 x 3^4

the quick trick is to add 1 to each exponent

4+1 and 4 +1

then multiply them 5 x 5 = 25
Director
Joined: 01 May 2007
Posts: 793

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11 May 2008, 07:04
very cool trick...and this always works to find the # of factors from the # of prime factors?
Senior Manager
Joined: 19 Mar 2008
Posts: 351

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26 Jul 2008, 10:25
How many factors does 36^2 have?
2
8
24
25
26
Director
Joined: 10 Sep 2007
Posts: 938

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26 Jul 2008, 11:07
36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 5*5 = 25

Senior Manager
Joined: 19 Mar 2008
Posts: 351

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26 Jul 2008, 23:28
abhijit_sen wrote:
36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 5*5 = 25

You answer is correct. Could you explain in more details. I still not understand. Thanks.
Manager
Joined: 15 Jul 2008
Posts: 206

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28 Jul 2008, 05:22
1
KUDOS
The general rule...
For finding the number of factors for any given number first break it down into powers of prime factors. pf1^a, pf2^b,......

Now, the total number of factors = (power of pf1 + 1) * (power of pf2 + 1)*...... or (a+1)*(b+1)*....

eg. let us say u want to find the number of factors of 12. 12=2*2*3 = 2^2 * 3^1 pf1=2 pf2=3 a=2 b=1
total number of factors = (a+1)(b+1) = (2+1)*(1+1) = 6
1,2,3,4,6,12 are the 6 factors of 12.
Senior Manager
Joined: 19 Mar 2008
Posts: 351
Forgot an important shortcut, pls help! [#permalink]

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28 Aug 2008, 07:56
How many factors does 36^2 have?

OA is 25.

36^2 = 2^4 x 3^4

Instead of listing out the factors, there was a equation for shortcut to calcluate the total number of factors.

But I forgot, do you guys know?

Tks
Manager
Joined: 15 Jul 2008
Posts: 206
Re: Forgot an important shortcut, pls help! [#permalink]

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28 Aug 2008, 08:27
1
KUDOS
judokan wrote:
How many factors does 36^2 have?

OA is 25.

36^2 = 2^4 x 3^4

Instead of listing out the factors, there was a equation for shortcut to calcluate the total number of factors.

But I forgot, do you guys know?

Tks

(4+1)*(4+1).
it is the product of all (powers of prime factors + 1)

Last edited by bhushangiri on 28 Aug 2008, 08:28, edited 1 time in total.
Director
Joined: 10 Sep 2007
Posts: 938
Re: Forgot an important shortcut, pls help! [#permalink]

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28 Aug 2008, 08:27
1
KUDOS
If a number can be represented as a^x*b^y*c^z, where a, b, and c are prime factors.
Then total number of factors are (x+1)*(y+1)*(z+1).
SVP
Joined: 07 Nov 2007
Posts: 1799
Location: New York
Re: Forgot an important shortcut, pls help! [#permalink]

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28 Aug 2008, 08:40
judokan wrote:
How many factors does 36^2 have?

OA is 25.

36^2 = 2^4 x 3^4

Instead of listing out the factors, there was a equation for shortcut to calcluate the total number of factors.

But I forgot, do you guys know?

Tks

2^0 2^1 ... 2^n ---> (n+1) factors
3^0 3^1 ... 3^n ---> (n+1) factors

Total factors.. combination of both = (n+1)(n+1)
_________________

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Re: Forgot an important shortcut, pls help!   [#permalink] 28 Aug 2008, 08:40

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