If both 11^2 and 3^3 are factors of the number
a * 4^3 * 6^2 * 13^11, then what is the smallest possible value of 'a'?

Question

If both 11^2 and 3^3 are factors of the number 
a * 4^3 * 6^2 * 13^11, then what is the smallest possible value of 'a'?

ash2326 · Answer

It's given that 11^2 and 3^3 are the factors of the number. Let's try to find these factors here!!!

anonymous · Answer

yeah plz help me ash2326

anonymous · Answer

Let's start by writing the gven no in form of prime numbers. Basically, write 6^2 in terms of 3 and 2

anonymous · Answer

*given

anonymous · Answer

ok then

ash2326 · Answer

We have
$$a *4^3  6^2  13^{11}$$
We can see 6^2 here, let's write 6 as 3*2 and then We'll find a
$$a4^32^23^213^{11}$$
Here 3^2 is there but we need 3^3 as a factor so a will have a 3

ash2326 · Answer

I meant one of the factors of a is 3

anonymous · Answer

i feel i got the solution shall i try to answer

anonymous · Answer

Yes as @ash2326  wrote.  Now according to the question, the number should have 11^2 and 3^2 as its factors.  If we see the number right now. It only has one 3 .  So 
a should basically be 3 * 11^2

ash2326 · Answer

@shivam_bhalla thanks for completing the solution:)

anonymous · Answer

ty ash and shivam for helping me out

anonymous · Answer

Welcome :) and thanks @ash2326  :)

ash2326 · Answer

You're welcome @dark_knight 
and 
$$\Huge \text{ Welcome to Open Study}$$\

anonymous · Answer

thanks ash can i ask one more question

ash2326 · Answer

Yeah but close this one first and post the other as new question

anonymous · Answer

i have already closed this question.

anonymous · Answer

He meant close this question and post the new question separately