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# Factors

Author Message
Manager
Joined: 14 Jul 2010
Posts: 71

Kudos [?]: 34 [0], given: 2

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15 Aug 2010, 06:29
00:00

Difficulty:

(N/A)

Question Stats:

50% (01:48) correct 50% (10:05) wrong based on 3 sessions

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If n is 2^5*3^4*5^3*7^2, How many factors does n has?

16
32
48
120
720

Kudos [?]: 34 [0], given: 2

Intern
Joined: 17 Jul 2010
Posts: 15

Kudos [?]: 4 [2], given: 23

### Show Tags

15 Aug 2010, 06:44
2
KUDOS
efet wrote:
If n is 2^5*3^4*5^3*7^2, How many factors does n has?

16
32
48
120
720

For this kind of questions, remember a formula:

[highlight]If the prime factorization of a number is in the form of a^x*b^y*c^z, then the

Number of factors = (x+1)*(y+1)*(z+1)[/highlight]

Now, coming to the given question,
number of factors = (5+1)*(4+1)*(3+1)*(2+1) = 6*5*4*3 = 360

Please check if the question you posted is correct and what is the source of the question.

Kudos [?]: 4 [2], given: 23

Manager
Joined: 14 Jul 2010
Posts: 71

Kudos [?]: 34 [0], given: 2

### Show Tags

15 Aug 2010, 06:48
maanavrelan4gmat, great formula. I wish I knew it before.

Kudos [?]: 34 [0], given: 2

Re: Factors   [#permalink] 15 Aug 2010, 06:48
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