Q.Write the smallest didgit and the …

1. (a) Divisibility rule of 3: A number is divisible by 3 if sum of all the digits of the number is divisible by 3.

Here, _ + 6 + 7 + 2 + 4 = _ + 19

Therefore, the smallest digit is 2 so that the total will be 2 + 19 = 21, which is divisible by 3. So now, 26724 is divisible by 3.

Also, the greatest digit is 8 so that the total will be 8 + 19 = 27, which is divisible by 3, so now 86724 is divisible by 3.

    (b) Divisibility rule of 3: A number is divisible by 3 if sum of all the digits of the number is divisible by 3.

Here 4 + 7 + 6 + 5 + _ + 2 = _ + 24

Therefore, the smallest digit is 0 so that the total will be 0 + 24 = 24, which is divisible by 3. So now, 476502 is divisible by 3.

Also, the greatest digit is 9 so that the total will be 9 + 24 = 33, which is divisible by 3, so now 476592 is divisible by 3.

2. (a) Divisibility rule of 11: A number is divisible by 11 if the difference of the sums of digits of even places and that of odd places is either 0 or divisible by 11.

Here, Sum of even places = 8 + _ + 9 = 17 + _ and Sum fo odd places = 2 + 3 + 2 = 7

Therefore, the required digit is 1, so that the difference will be 18 - 7 = 11 and the number 921382 is divisible by 11

    (b) Divisibility rule of 11: A number is divisible by 11 if the difference of the sums of digits of even places and that of odd places is either 0 or divisible by 11.

Here, Sum of even places = 8 + 9 + 8 = 25 and Sum fo odd places = 4 + 4 + _ = 8 + _

Therefore, the required digit is 6, so that the difference will be 25 - 14= 11 and the number 869484 is divisible by 11.