# GMAT Hard Quant Question 38 | Arithmetic

###### Product of Factors | Number Properties Practice | GMAT Sample Questions

The given question is a challenging GMAT hard quant problem solving question testing concepts in number properties - Product of factors of cubes and squares of numbers.

Question 38: What is the product of all the factors of the cube of a positive integer 'n' if the product of all the factors of square of n is n3?

1. n4
2. n6
3. n9
4. n5
5. Cannot be determined

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### Explanatory Answer | GMAT Number Properties

'n' is a positive integer.
Product of the factors of n2 is n3.

If the product of the factors of n2 = n3, the only factors of n2 are 1, n, and n2.
So, we can infer that n does not have any factor other than 1 and itself.
Therefore, n is a prime number.

Factors of n3 if n is a prime number are 1, n, n2 and n3.
So, the product of the factors of n3 = 1 × n × n2 × n3 = n6

##### Choice B is the correct answer.

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