Answers and Solutions

Answer

1.The nos  divisible by 2 are148,342,510,616,840,918,1440(all are even nos).

The nos divisible by 3 are342,405,510,840,918,1440(the sum of the nos are divisible by 3)

The nos divisible by 10 are510,840,1440(the last digit of the nos are 0)

2.The nos divisible by 3 are  342,405,510,918.

The nos divisible  by 4 are 128 only.(the last two digits are divisible by 4)

The nos divisible by 9 are 342,405,918(the sum of the digits are divisible by 9)

Answer

1) Divisible by 2: 128,342,510,616,840,918,1440     Divisible by 3: 342,405,510,840,918,1440     Divisible by 10: 510,840,1440

2) Divisible by 3: 342,405,510,918.     Divisible by 4: 128     Divisible by 9: 342,405,918     Divisible by 3,4 or 9: 128,342,405,510,918

Answer

1)    Divisible by 2 : 128, 342, 510, 616, 840, 918, 1440.

       Divisible by 3 : 342, 405, 510, 840, 918, 1440.

       Divisible by 10 :   510, 840, 1440.

       1523 is not divisible by given numbers. 

2 )  Divisible by 3 : 342, 405, 510, 918.

      Divisible by 4 : 128 only.

      Divisible by 9 : 342, 405, 918.

Answer

Answer:

Divisibility test:

 i)    for  2:   All  even numbers are  divisible by 2.

ii)    for  3:   If the sum of the digits of the given number is divisible by 3,then the number is divisible by 3.

iii)   for 4:    If the last two  digits of the given number are  divisible by 4,then the number is divisible by 4.

iv)   for 9:    If the sum of the digits of the given number is divisible by 9,then the number is divisible by 9.

 v)   for 10:  All numbers ending with 0 are divisible by 10.

Note:   If a number is divisible by 9 then it is also divisible by its sub multiple 3.

As per the above divisibility rule the set of numbers

a) 128, 342,405,510,616,840,918,1440,1523  can be grouped on the basis of divisibility by 2,3,10as below:

128,616: Both are  even numbers and hence they are divisible by 2

 405: This  is an odd number and so not divisible by 2. But the sum of its digits add up to 9 which is

          divisible by 3. Hence 405 is divisible by 3.

 342,918 :Both are even and so divisible by 2.Further the sum of their digits  (9,18)  are divisible by 3 and

                  hence  they are divisible also by 3.Hence these 2 numbers are divisible by both 2 &3..

510,840,1440:  All the three numbers are even and so divisible by 2.Sum of the digits of all the three numbers are divisible by 3 and so these three numbers are also divisible by 3.Further ,the last digit of all the three numbers is 0 and so these three numbers are also divisible by 10 .Thus these three numbers are divisible by 2,3&10.

1523 : This number  cannot be grouped into any of the above as it is not divisible byany of the numbers  2,3,10.

The results are summarised below:

Divisible by 2 only:      128,616

Divisible by 3 only:       405

Divisible by 2&3:          342,918

Divisible by 2,3,10:       510,840,1440

Not divisible by any of the above: 1523:               

b)  128, 342, 405,510,918 can be grouped on the basis of divisibility by 3,4,9 as below:

510:  The sum of the digits of this number is 6 which is divisible by 3 and so this number is divisible by 3 .

128:   The last two digits of this number is 28 , which is divisible by 4.So this number is divisible by 4.

342,405,918: The sum of the digits of this number are 9,9 and 18  and all are divisible by 9.Hence these three numbers are divisible by 9.As 3 is a sub multiple of 9,these numbers are also divisible by 3.

Hence these three numbers are divisible by both 3&9.  

The results are summarised below:

Divisible by 3 only;       510

Divisible by 4 only:       128

Divisible by both 3&9:   342,405,918,