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

Question

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

chetan2u · Accepted Answer

Hi,
 we are basically looking at 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

mathiaskeul · Answer

I'd say the answer is 1 because every divisor is just a multiple of the original prime?

mathiaskeul · Answer

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

Thank you!

chetan2u · Answer

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

Bunuel · Answer

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

stonecold · Answer

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 .

JeffTargetTestPrep · Answer

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.

Answer: D

pratiksha1998 · Answer

Since we know that n is a prime number, and the formula for finding the number of factors for any number N is
N = a^x X b^y....., where a and b are the prime factors
number of factors = (x+1)X(y+1).

Therefore for this question the answer would be (3+1) = 4
Option D

+Kudos, if this explanation helps

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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

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