Question

4. Product of two numbers is 6300 and their HCF is 15 find the smaller number
a)450
b)320
c)430
d)420​

Answer 1

Answer:

$420$

Let the two numbers be x and y respectively.

It is given that the product of the two numbers is 6300, therefore,

      

xy=6300

Also 15 is their HCF, thus both numbers must be divisible by 15.

So, let x=15a and y=15b, then  

$15a \: \times 15b = 6300 \\ 225ab = 6300 \\ ab = \frac{6300}{225} \\ ab = 28$

Therefore, required possible pair of values of x and y which are prime to each other are (1,28) and (4,7).

Thus, the required numbers are (15,420) and (60,105).

Hence, the number of possible pairs is 2.