question_answer 22)

Write the smallest digit and the greatest digit in the blank space of each of the following numbers, so that the number formed is divisible by 3: (a) ____ 6724                    (b) 4765 ____ 2 TIPS Firstly, find the sum of digits of given number, then subtract it from those multiples of 3, which are greater than this sum to get smallest and greatest digit.

Answer:

                (a) We have, ____ 6274 Sum of the given digits = 6 + 7 + 2 + 4 = 19 \[\because \] Multiples of 3 greater than 19 are 21, 24, 27, 30, ... \[\therefore \]21 ? 19 = 2; 24 ? 19 = 5; 27 ? 19 = 8; 30 -19 = 11 But 11 is not a single digit. \[\therefore \] Smallest digit = 2 and greatest digit = 8 (b) We have, 4765 ____ 2 Sum of the given digits = 4 + 7 + 6 + 5 + 2 = 24 \[\therefore \] 24 is a multiple of 3, so smallest digit = 0 Now, multiples of 3 greater than 24 are 27, 30, 33, 36, ... \[\therefore \]27 ? 24 = 3; 30 ? 24 = 6; 33 ? 24 = 9; 36 ? 24 = 12 But 12 is not a single digit. \[\therefore \] Smallest digit = 0 and greatest digit = 9