p&cq11

[Saumyojit]

If "a" is a factor of 120, then find the no of positive integral solutions of X1.X2.X3=a


No of factors of 120 =16. (1,2,3,4,5,6,8,10...120)
Now how to proceed?

 

[pka]

If "a" is a factor of 120, then find the no of positive integral solutions of X1.X2.X3=a


No of factors of 120 =16. (1,2,3,4,5,6,8,10...120)
Now how to proceed?

In factored form, [imath]120=2^3\cdot 3\cdot 5[/imath] so there are [imath](3+1)(1+1)(1+1)=16[/imath] divisors.

 

[Cubist]

If "a" is a factor of 120

Therefore, a*b=120, call this equation "C", where both a and b are positive integers.

find the no of positive integral solutions of X1.X2.X3=a

Can you combine the equation in this quote with equation "C" to give something in a form that you already know how to solve?

 

[Dr.Peterson]

If "a" is a factor of 120, then find the no of positive integral solutions of X1.X2.X3=a


No of factors of 120 =16. (1,2,3,4,5,6,8,10...120)
Now how to proceed?

The wording is odd. I suppose this means that x₁ x₂ x₃ can be any divisor of 120. If so, you might just think of it as asking for the number of positive integer solutions of x₁ x₂ x₃ x₄ = 120. [Maybe this is the same idea Cubist has.]

Why do you think the number of divisors of 120 (which of course you got correctly) is relevant?

 

[Cubist]

just think of it as asking for the number of positive integer solutions of x₁ x₂ x₃ x₄ = 120. [Maybe this is the same idea Cubist has.]

Nope, my idea was (a)*b=120 => (x₁ x₂ x₃) b = 120

Don't worry, I know this is actually the same as your suggestion. I'm impressed that you were able to see this directly using logical thinking!

 

[Saumyojit]

Nope, my idea was (a)*b=120 => (x₁ x₂ x₃) b = 120

Don't worry, I know this is actually the same as your suggestion. I'm impressed that you were able to see this directly using logical thinking!

120 divisors is irrelevant .
a*b =120
Where I got stuck.

Otherwise the question is easy

 

[Dr.Peterson]

120 divisors is irrelevant .
a*b =120
Where I got stuck.

Otherwise the question is easy

So what have you tried at that point? This is your exercise to do, not ours.

We've given you at least one idea. Do you understand it? It's a simple extension of a problem we discussed before.

And can you tell us where the problem came from, how it was worded exactly, and whether you have an answer to compare yours to?

 

[Saumyojit]

Do you understand it? It's a simple extension of a problem we discussed before.

Absolutely.
The same as previous one

 

[Dr.Peterson]

Absolutely.
The same as previous one

So you've solved it? Please show your work.