Give an example of a six-digit natural number that can only be written as 2 and 0 and is divisible by 24.

According to the rule of division, the dividend is divided by an ambiguous divisor without a remainder if the sum of the numbers of the dividend is divided by coprime factors obtained during the decomposition of the divisor.

Let us expand 24 into prime factors:

24 = 2 * 2 * 2 * 3 = 8 * 3.

8 and 3 are relatively prime factors (8 is not divisible by 3, but 3 by 8).

Obviously, a six-digit number should have only 3 twos, so that it contains both twos and zeros, and, according to the rule of division, is divisible by 3.

For a number to be divisible by 8, there must be 00 at the end of a six-digit number, since 20 and 2 are not divisible by 8, 200 is divisible by 8.

That is, the first in the six-digit number must be the number 2, and at the end 00.

In the middle of the desired number, there are two more digits 2 and one digits 0.

Let’s list the possible options:

222000, 220200, 202200.

Answer: 202200.