What number should be put instead of an asterisk in the number 51 * 8 there so that it is divisible by 4 and 9?

Let’s recall the criteria for divisibility by 4 and 9:

a number is divisible by 4 if its last two digits are divisible by 4;
a number is divisible by 9 if the sum of its digits is divisible by 9.

The desired number must be divisible by 4 and 9, which means that instead of * in the number 51 * 8, you need to put such a figure so that both signs are fulfilled.

Let’s find the sum of the known digits of the number 51 * 8:

5 + 1 + 8 = 14.

In order for the sum of the digits of 51 * 8 to be divisible by 9, instead of *, you need to substitute such a digit so that the sum of 14 and this digit is divisible by 9. The only digit 4 that matches this condition: 14 + 4 = 18, 18 is divisible by 9.

The number 5148 ends with 48, 48 is divisible by 4, which means that the number 5148 is divisible by 4.

Answer: 4.