Question

Find the number of ways in which a number 288 can be expressed as a product of two factors

Answer 1

both the no are 144
I am sure

Answer 2

Answer:

The number of ways in which a number 288 can be expressed as a product of two factors is 9

Step-by-step explanation:

In order to find the number of ways in which a number can be expressed as a product of two factors we follow :

Firstly do the  prime factorisation of given number and  convert the factors in the form of  $x^{p}$ $y^{q}$

where x, y are prime factors and the p,q are their powers.

Then, we find  number of factors which can be expressed as ( p+1 ) * ( q+1 )

Finally,

The number of ways in which a number can be expressed as a product of two factors is calculated as ( p + 1 ) ( q + 1 ) / 2

So now for our question,

we need to express 288 as a product of two factors

Prime factorisation of 288 = 2 * 2 * 2 * 2 * 2 * 3 * 3

Expressing it in form of $x^{p}$ $y^{q}$  = $2^{5}$ $3^{2}$

Then,

number of factors = ( p + 1 ) ( q+1 )

= ( 5 + 1 ) ( 2 + 1 )

= ( 6 ) * ( 3 )

= 18

Finally ,

Number of ways to represent =  ( p + 1 ) ( q+1 ) / 2

⇒ 18 / 2 = 9

Hence,

The number of ways in which a number 288 can be expressed as a product of two factors is 9