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6. Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11 :
   (a) 92 __ 389             (b) 8 __ 9484.

(a) 92 __ 389 Sum of odd digits = 9 + (blank space) + 8 = 17 + blank space Sum of even digits = 2 + 3 + 9 = 14 As we know, The number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is divisible by 11. If we make the sum of odd digits = 25 then we will have difference = 25 - 14 = 11 which is divisible by 11. To make the...

5. 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

(a) _6724 Sum of the remaining digits = 19 To make the number divisible by 3, the sum of its digits should be divisible by 3. The smallest multiple of 3 which comes after 19 is 21. Therefore, smallest number = 21 - 19 - 2 Now, 2 + 3 + 3 = 8 If we put 8, then the sum of the digits will be 27 and as 27 is divisible by 3, the number will also be divisible by 3. Therefore, the largest number is...

4. Using divisibility tests, determine which of the following numbers are divisible by 11:
(a) 5445        (b) 10824       (c) 7138965        (d) 70169308         (e) 10000001
(f) 901153

(a) 5445 Sum of the digits at odd places = 5 + 4 = 9 Sum of the digits at even places = 4 + 5 = 9 Difference = 9 - 9 = 0 As the difference between the sum of the digits at odd places and the sum of the digits at even places is O, therefore, 5445 is divisible by 11. (b) 10824 Sum of the digits at odd places = 4 + 8 + 1 = 13 Sum of the digits at even places = 2 + 0 = 2 Difference = 13 - 2 = 11...

3. Using divisibility tests, determine which of following numbers are divisible by 6:
(a) 297144        (b) 1258             (c) 4335       (d) 61233        (e) 901352   
(f) 438750         (g) 1790184       (h) 12583     (i) 639210        (j) 17852

(a) 297144  Since the last digit Of the number is 4, it is divisible by 2. On adding all the digits of the number, the sum obtained is 27. Since 27 is divisible by 3, the given number is also divisible by 3. As the number is divisible by both 2 and 3, it is divisible by 6. (b) 1258 Since the last digit of the number is 8, it is divisible by 2. On adding all the digits of the number, the sum...

2. Using divisibility tests, determine which of the following numbers are divisible by 4; by 8:
(a) 572        (b) 726352         (c) 5500            (d) 6000        (e) 12159
(f) 14560     (g) 21084           (h) 31795072     (i) 1700         (j) 2150

A number with 3 or more digits is divisible by 4 if the number formed by its last two digits is divisible by 4. A number with 3 or more digits is divisible by 8 if the number formed by its last three digits is divisible by 8.   a)      572 72 is divisible by 4, hence the number is divisible by 4. The number is not divisible by 8.   b)      726352 52 is divisible by 4, hence the number is...

1. Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10 ; by 11 (say, yes or no):
                                   

Number                              Divisible...
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