Question

In how many ways 450 can be written as product of two numbers aptitude

Answer 1

Answer:

Step-by-step explanation:

I think you are interested only in natural numbers (for reals and integers the answer is different, of course), so that will be assumed.

A nice way of calculating it is finding the number of divisors of $450$, because for each divisor $n$ of $450$, such a product is determined, once $450 = \frac{450}{n} \cdot n$. But as product of natural numbers is commutative, that is, $\frac{450}{n} \cdot n = n \cdot \frac{450}{n}$, this procedure will be counting twice the same product. So, at the ending of this calculation, we need to divide the number we get by 2.

Note that $450 = 2^1\cdot 3^2 \cdot 5^2$. Then for each product of the prime factors we will find a divisor (for example, $2\cdot 3^2$ is a divisor, just as $2\cdot 3 \cdot 5$, so we just need to play with their exponents). There are two options for the exponent of 2 (0 or 1), three options for the exponent 3 (0, 1 or 2) and three options for the exponent of 5 (0, 1 or 2). So 450 have $2 \cdot 3 \cdot 3 = 18$ divisors. Then, as remarked above, 450 can be written as product of two numbers in $\frac{18}{2}  = 9$ ways.

Answer 2

Answer:

9 Ways

Step-by-step explanation:

450 = 2 * 3 *  3 * 5 * 5

450 = 2¹ * 3²  * 5²

Number of Factors = ( 1 + 1) * (2 + 1) * (2 + 1)

= 2 * 3 * 3

= 18

Each multiplication Will need Two Factors

so number of Ways = 18/2 = 9

Below are 9 ways

1 * 450

2 * 225

3 * 150

5 * 90

6 * 75

9 * 50

10 * 45

15 * 30

18 * 25

All further nultiplications will be repated only

25 * 18 , 30 * 15......................................, 450 *1  

Hence 9 Ways