[thehappypm]

The simple explanation is just that lot of ways that numbers can multiply to produce the same product

Like an odd number x times an even number y, x* y produces the same product as x* 2 and y/2

Same for a multiple of 3 c and and a non multiple of 3 d, c * d = c/3 * d*3

[danbruc]

This is just looking at it from a different perspective. Both, one 64 bit integer and the product of two 32 bit integers represent a number up to 2^64 with 64 bits. But while all 64 bit integers are unique, there are, as you say, several representation for some numbers as the product of two 32 bit integers and therefore it is impossible to represent all 64 bit integers. Commutativity alone costs you about 50 percent of all numbers in the range as x * y and y * x represent the same 64 bit number but with two different representation as a product of two 32 bit numbers, at least if x and y are different. But this tells you nothing about the numbers that you can not represent, only that they must exist. I was looking at it from this other perspective, which numbers are not representable as a product and why.