Question

In how many ways can a number 6084 be written as a product of two different factors ?

Answer 1

the correct answer is infinite Times for example if you take first number as x then second will be 6084/x. ask if any doubt

Answer 2

Answer:

The number of ways in which 6084 can be expressed as a product of two different factors is 13.

Step-by-step explanation:

To find : In how many ways can a number 6084 be written as a product of two different factors ?

Solution :

First we factor 6084:

$6084 = 2^2 \times 3^2 \times 13^2$

We know that,

If $N = a^p b^q c^r$, where a,b,c are primes,

Number of factors is represented by :  (p+1)(q+1)(r+1)

⇒ (2+1)(2+1)(2+1) = 27

Number of Ordered pairs of any two factors is  $\frac{(27+1)}{2}=14$

Since 6084 is a perfect square, evidently the ordered pair (78,78) is also counted in the above 14 pairs.

So, The number of ways in which 6084 can be expressed as a product of two different factors is 13.