Remainders for 5 and 6:
The number could be thirty, because five and six are both equivalent to thirty. Another answer it could be is sixty or anything that is a multiple of thirty. A rule that we found was that the answer had to end in a zero because there is no multiple of six that ends in a five. So we knew that the answer had to end in a zero, also multiples of five have to end in a five or zero.
Remainders for 4, 5 and 6:
The number could be sixty, because four, five and six are all equivalent to the number. Another answer it could be is one hundred and twenty or any multiple of sixty and above. The rule is that the number can only end in a zero because four and six do not have any multiple that ends in a five. Additionally, multiples of five can only end in a five or zero but their other companions cannot end in a five so the only number that the answer can end in is zero.
A pattern that we found in both of the questions was that all the answers end in a zero, because the other multiples besides five cannot end in a five so the only number that they have in common is zero.