Explanation:
x×y = 363
the highest (or greatest) common factor of x and y is 11.
that means we can divide x and y by 11 without remainder.
so,
x/11 × y = 363/11 = 33
x/11 × y/11 = 33/11 = 3
let's call the remaining factors of x and y :
a = x/11
b = y/11
and that means
ab = 3
as factors of natural numbers a and b must be natural numbers too. and they need to be factors of 3 (as their product is 3).
the only factors of 3 are 1 and 3.
we can therefore say (it does not matter which number is x and which is y) :
1 = x/11
x = 1×11 = 11
3 = y/11
y = 3×11 = 33
the greater number is 33.