naturewild, I shall attempt the second problem first.

**When an integer is divided by 15, the remainder is 7. **

Therefore, the number is of the form 15n+7, where n is a certain Natural number. When 15n+7 is divided by 5, since 15n is divisible by 5, the remainder is what it would be when 7 is divided by 5, hence, the remainder is 2.When 15n+7 is divided by 3, since 15n is divisible by 3, the remainder is what it would be when 7 is divided by 3, hence the remainder is 1.