In each of the following replace '*' by (i) the smallest digit (ii) the greatest digit so that the number formed is divisible by 3:

(a) 4*672

(b) 4756*2

For a number to be divisible by 3, the sum of its digits must be divisible by 3.

(a) 4*672

Sum of given digits (except *) = 4 + 6 + 7 + 2 = 19.

We need 19 + * to be divisible by 3.

The values of * which make 19 + * divisible by 3 are 2 (gives 21), 5 (gives 24) and 8 (gives 27).

(i) The smallest digit is 2. The number formed is 42672.

(ii) The greatest digit is 8. The number formed is 48672.

(b) 4756*2

Sum of given digits (except *) = 4 + 7 + 5 + 6 + 2 = 24.

We need 24 + * to be divisible by 3.

The values of * which make 24 + * divisible by 3 are 0 (gives 24), 3 (gives 27), 6 (gives 30) and 9 (gives 33).

(i) The smallest digit is 0. The number formed is 475602.

(ii) The greatest digit is 9. The number formed is 475692.