Question

If sum of two smallest factors and two largest factors of a number Nare 5 and 90 respectively, then find the value of N.​

Answer 1

Answer:

Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.

Negative Factors of 90: -1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45 and -90.

Prime Factors of 90: 2, 3, 5.

Prime Factorization of 90: 2 × 3 × 3 × 5 = 2 × 32 × 5

Sum of Factors of 90: 234.

Value of N is 234

Answer 2

Given: Sum of 2 smallest factor and 2 largest factors of a number N are 5 and 90 respectively

To Find : The value of N

Solution :-

Know that, Any number N can be expressed in the form of product of their prime factors.

Consider the followinf cases.

Case 1: Take 1 as one of the smallest factor and largest factors N is also included :-

Understand that, according to the question, sum of the two smallest factor is 5.

$\[\begin{array}{l}1 + x = 5\\ \Rightarrow x = 4\end{array}\]$

Therefore, if $x = 4$, number N Should be divisible by 2 also. Then, the two smallest factors will be 1 and 2.

$\[ \Rightarrow 1 + 2 \ne 5\]$

 Case 2: If smallest factors 1 is not included and in two largest factors N is included, Sum of 2 smallest factors of N $= 5$

Take the smallest factor as 2.  

Therefore,

Two smallest factors should be 2 and 3 respectively. as, ${ 2 + 3 = 5 } .$

Understand that from the question,   Sum of two largest factors of $N = 90$

$\[\begin{array}{l}N + \left( {\frac{N}{2}} \right) = 90\\ \Rightarrow \frac{{3N}}{2} = 90\\ \Rightarrow N = \frac{{180}}{3}\\ \Rightarrow N = 60\end{array}\]$

 

Check whether sum of two smallest and two largest numbers are 5 and 90 respectively.

Factors of 60 are $= 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30$and $60$.

Therefore,

Sum of smallest two factors (Other than 1) , $2 + 3 = 5$.

Sum of largest two factors, $30 + 60 = 90$ .

Hence, value of N is equal to 60 .