Question

Product of three natural numbers is $24000$ and their HCF is $10$ How many such triplets of numbers are there?

• A. $5$
• B. $4$
• C. $6$
• D. $7$

Answer 1

The correct option is A $5$

Let the numbers be $10a,10b$ and $10c$.

It is given that the product of three natural numbers is $24000$, therefore we have,

$10a\times 10b\times 10c=24000\Rightarrow 1000abc=24000\Rightarrow abc=\frac{24000}{1000}\Rightarrow abc=24$

Thus, the values of $(a,b,c)$ can be $(1,1,24),(1,2,12),(1,3,8),(1,4,6)$ and $(2,3,4)$.

Therefore, the required numbers are $(10,10,240),(10,20,120),(10,30,80),(10,40,60)$ and $(20,30,40)$.

Hence, the number of triplets are $5$.