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# how many divisors does 256 have? 349? i didn't get these

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Manager
Joined: 04 May 2007
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how many divisors does 256 have? 349? i didn't get these [#permalink]  19 May 2007, 09:38
how many divisors does 256 have? 349?

i didn't get these questions from a book; i just seem to run into these sorts of questions a lot and i always waste my time figuring them out... i was just wondering if there was a like a number theory way to figure them out without listing everything.
Director
Joined: 26 Feb 2006
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Re: divisors [#permalink]  19 May 2007, 09:45
gmatiscoming wrote:
how many divisors does 256 have? 349?

i didn't get these questions from a book; i just seem to run into these sorts of questions a lot and i always waste my time figuring them out... i was just wondering if there was a like a number theory way to figure them out without listing everything.

i do factorization starting from 2, 3 and so on.
VP
Joined: 08 Jun 2005
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Me too - factoring

256 : 2
128 : 2
64 : 2
32 : 2
16 : 2
8 : 2
4 : 2
2

2*2*2*2*2*2*2*2 = 256

so divisors for 256 are 2,4,8,16,32,64,128

349 is a prime number !

so divisors for 349 are 1 & 349

Manager
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lol, i just picked 349 off the top of my head, didn't mean to pick a prime.

squirrel, what about 1? 256 has 9 factors.

I found a 'number theory' method... don't know if it is much faster or if it can be proven true for all #'s

check this out:

how many factors does 120 have?

step 1:
get it down to primes

2^3 * 3 * 5

take the exponents of the primes and add 1 to them and multiply them

3+1 * 1+1 * 1+1 =16
VP
Joined: 08 Jun 2005
Posts: 1146
Followers: 6

Kudos [?]: 136 [0], given: 0

gmatiscoming wrote:
lol, i just picked 349 off the top of my head, didn't mean to pick a prime.

squirrel, what about 1? 256 has 9 factors.

I found a 'number theory' method... don't know if it is much faster or if it can be proven true for all #'s

check this out:

how many factors does 120 have?

step 1:
get it down to primes

2^3 * 3 * 5

take the exponents of the primes and add 1 to them and multiply them

3+1 * 1+1 * 1+1 =16

Yes ! you are right , including 1 & 256 --- nine divisors

if you ask me I would apply KISS (Keep It Simple, Stupid)

under pressure - 'number theory' can throw you off.

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