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# If n is a prime number between 0 and 100, how many positive divisors

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If n is a prime number between 0 and 100, how many positive divisors  [#permalink]

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20 Apr 2016, 01:03
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If n is a prime number between 0 and 100, how many positive divisors does n^3 have?

A. 1
B. 2
C. 3
D. 4
E. 5

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Re: If n is a prime number between 0 and 100, how many positive divisors  [#permalink]

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20 Apr 2016, 02:37
I'd say the answer is 1 because every divisor is just a multiple of the original prime?
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Re: If n is a prime number between 0 and 100, how many positive divisors  [#permalink]

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20 Apr 2016, 02:51
3
I'd say the answer is 1 because every divisor is just a multiple of the original prime?

Hi,
we are basically looking it factors of$$n^3,$$ where n is a PRIME number..
number of factors $$= (3+1) = 4.$$.
we can also write them down.
1, n, $$n^2$$, and $$n^3$$
so ans will be 4
D
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Re: If n is a prime number between 0 and 100, how many positive divisors  [#permalink]

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20 Apr 2016, 02:57
chetan2u wrote:
I'd say the answer is 1 because every divisor is just a multiple of the original prime?

Hi,
we are basically looking it factors of$$n^3,$$ where n is a PRIME number..
number of factors $$= (3+1) = 4.$$.
we can also write them down.
1, n, $$n^2$$, and $$n^3$$
so ans will be 4
D

Hi chetan. Could you explain the rule for this? Is it only for prime numbers?

Thank you!
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Took the Gmat and got a 520 after studying for 3 weeks with a fulltime job. Now taking it again, but with 6 weeks of prep time and a part time job. Studying every day is key, try to do at least 5 exercises a day.

Math Expert
Joined: 02 Aug 2009
Posts: 6797
If n is a prime number between 0 and 100, how many positive divisors  [#permalink]

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20 Apr 2016, 03:03
chetan2u wrote:
I'd say the answer is 1 because every divisor is just a multiple of the original prime?

Hi,
we are basically looking it factors of$$n^3,$$ where n is a PRIME number..
number of factors $$= (3+1) = 4.$$.
we can also write them down.
1, n, $$n^2$$, and $$n^3$$
so ans will be 4
D

Hi chetan. Could you explain the rule for this? Is it only for prime numbers?

Thank you!

Hi,

when ever you are looking for the number of factors/positive divisors, get the integer in its simplest form/scientific notation ..
for example say 36..
$$36 = 2^2*3^2$$.. ans will be (2+1)(2+1) = 3*3=9..
$$120 = 2^3*3*5$$.. ans will be (3+1)(1+1)(1+1) = 4*2*2=16..

say a Q further asks you ODD factor of 120..
just drop the even 2-- (3+1)(1+1)(1+1) .. ans will be (1+1)(1+1)=2*2=4..
Even factors will be Total - ODD = 16-4=12..
May help somewhere
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Math Expert
Joined: 02 Sep 2009
Posts: 49271
Re: If n is a prime number between 0 and 100, how many positive divisors  [#permalink]

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20 Apr 2016, 03:05
chetan2u wrote:
I'd say the answer is 1 because every divisor is just a multiple of the original prime?

Hi,
we are basically looking it factors of$$n^3,$$ where n is a PRIME number..
number of factors $$= (3+1) = 4.$$.
we can also write them down.
1, n, $$n^2$$, and $$n^3$$
so ans will be 4
D

Hi chetan. Could you explain the rule for this? Is it only for prime numbers?

Thank you!

Finding the Number of Factors of an Integer:

First make prime factorization of an integer $$n=a^p*b^q*c^r$$, where $$a$$, $$b$$, and $$c$$ are prime factors of $$n$$ and $$p$$, $$q$$, and $$r$$ are their powers.

The number of factors of $$n$$ will be expressed by the formula $$(p+1)(q+1)(r+1)$$. NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: $$450=2^1*3^2*5^2$$

Total number of factors of 450 including 1 and 450 itself is $$(1+1)*(2+1)*(2+1)=2*3*3=18$$ factors.

Check for more here: math-number-theory-88376.html
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Re: If n is a prime number between 0 and 100, how many positive divisors  [#permalink]

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20 Apr 2016, 13:45
Two ways to solve this one
Pick has 2 => 8 has 4 factors hence D
next way to solve this up is using the formula => if K=P^a * Q^b * R^c where P,Q,R are primes ; then the number of divisors of K are => a+1 * b+1 * c+1

Hit that D option .
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Re: If n is a prime number between 0 and 100, how many positive divisors  [#permalink]

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02 Jul 2018, 10:02
Bunuel wrote:
If n is a prime number between 0 and 100, how many positive divisors does n^3 have?

A. 1
B. 2
C. 3
D. 4
E. 5

If let n = 2, then n^3 = 8, which has divisors of 1, 2, 4, and 8, so n^3 has 4 positive divisors. This concept holds for any prime number n^3. It is always/only divisible by 1, n, n^2, and n^3.

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Re: If n is a prime number between 0 and 100, how many positive divisors &nbs [#permalink] 02 Jul 2018, 10:02
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