Find the smallest natural number that, when divided by 5, gives a remainder of 4.

To find a number with these properties, let’s model this number.

Any natural number that, when divided by 5, gives a remainder of 4, can be written as follows:

5 * a + 4,

where a is any integer.

Substitute the smallest possible number for a, i.e. 0:

5 * 0 + 4 = 4.

Then dividing 4 by 5 gives 0 and the remainder is 4.

If it is necessary that there is an integer part during division, then substitute one instead of a:

5 * 1 + 4 = 9;
9: 5 = 1 (4 in the remainder).

Answer: 4 or 9 (depending on the condition).