representing multiple numbers by a single number? Is it possible to represent two numbers by a single number such that we can get both numbers back from it? 
This wouldn't be possible because if two numbers $a$ and $b$ are represented by $x$ then $a$, $b$ and $c$ can be represented as $x$ and $c$ and further as some number $y$, and so on,  
Now, $2^5 3^2$ ie. $288$ is a representative of $5$ and $2$ as we can easily get $5$ and $2$ by prime factorization of $288$, so can't any amount of number be represented by a single number in this manner,  
for example, a single number to represent a triangle completely
 A: The method you have already used can be adopted to represent lots of numbers by a single number.
For example, if you have integer coordinates $(a,b),(c,d),(e,f)$ for the vertices of a triangle, then the single number 
$$2^a3^b5^c7^d11^e13^f$$
represents the triangle unambiguosly.
I see this is virtually the same as the answer of @Matthew Daly but I am allowing negative integers as well to produce a representation by rational numbers.
A: You can represent any finite data structure (including lists of integer numbers) using a string of
characters in some standard format such as JSON. You can then interpret
the binary bit string  representation of this JSON
character string as the binary representation of a positive integer.
A key advantages of this approach is that it has no
need of the use of prime number factorization and it
can be represent any finite data structure and
not just lists of numbers. The OP did not specify
what kind of representation must be used, but
only gave a simple prime factorization example to
ask about its feasability.
A: You are correct that we can "encode" any finite list (of known length) of non-negative integers as a singe non-negative integer by the injection $$(a,b,c,...)\mapsto2^a3^b5^c...$$
Of course, this is taking advantage of the factorability of non-negative integers. You couldn't use the same mapping to encode real numbers, obviously.
