Exercise 15.3

1. Check whether the given numbers are divisible by ‘6’ or not?

(a) 273432

Solution:

For a number to be divisible by 6, it must be divisible by both and . 273432 is , so it's divisible by .

The sum of its digits is 2 + 7 + 3 + 4 + 3 + 2 = , which is divisible by .

Therefore, 273432 isis not divisible by 6.

(b) 100533

Solution:

100533 is , so it is notis divisible by 2.

Therefore, 100533 is notis by 6.

(c) 784076

Solution:

784076 is , so it's divisible by .

The sum of its digits is 7 + 8 + 4 + 0 + 7 + 6 = , which is notis divisible by 3.

Therefore, 784076 is notis divisible by 6.

(d) 24684

Solution:

24684 is , so it's divisible by 2.

The sum of its digits is 2 + 4 + 6 + 8 + 4 = , which isis not divisible by 3.

Therefore, 24684 isis not divisible by 6.

2. Check whether the given numbers are divisible by ‘4’ or not?

(a) 3024

Solution:

3024 is divisible by 4: YesNo

The last digits are , which is divisible by .

Therefore, 3024 is divisible by 4.

(b) 1000

Solution:

1000 is divisible by 4: Noyes

The last two digits are , which is divisible by .

Therefore, 1000 is divisiblenot divisible by 4.

(c) 412

Solution:

412 is divisible by 4: Yesno

The last two digits are , which is divisible by .

Therefore, 412 is divisible by 4.

(d) 56240

Solution:

56240 is divisible by 4: YesNo

The last two digits are , which is divisible by .

Therefore, 56240 is Divisible by 4.

3. Check whether the given numbers are divisible by ‘8’ or not?

(a) 4808

Solution:

4808 is divisible by 8: TrueFalse

The last digits are , which isisn't divisible by 8.

Therefore, 4808 is divisible by 8.

(b) 1324

Solution:

1324 is divisible by 8: TrueFalse

The last digits are , which isis not divisible by 8.

Therefore, 1324 is divisible by 8.

(c) 1000

Solution:

1000 is divisible by 8: TrueFalse

The last three digits are , which isis not divisible by 8.

Therefore, 1000 is divisible by 8.

(d) 76728

Solution:

76728 is divisible by 8: TrueFalse

The last three digits are , which isis not divisible by 8.

Therefore, 76728 is divisible by 8.

4. Check whether the given numbers are divisible by ‘7’ or not?

(a) 427

Solution:

Double the last digit: 7 × = . Subtract it from the remaining number: - = .

Since 28 isisn't divisible by 7, 427 isisn't divisible by 7.

(b) 3514

Solution:

Double the last digit: 4 × 2 = . Subtract it from the remaining number: - = .

Double the last digit: 3 × 2 = . Subtract it from the remaining number: - = .

Since 28 isisn't divisible by 7, 3514 isisn't divisible by 7.

(c) 861

Solution:

Double the last digit: 1 × 2 = . Subtract it from the remaining number: - = .

Since 84 isisn't divisible by 7, 861 isisn't divisible by 7.

(d) 4676

Solution:

Double the last digit: 6 × 2 = . Subtract it from the remaining number: - = .

Double the last digit: 5 × 2 = . Subtract it from the remaining number: - = .

Since 35 isisn't divisible by 7, 4676 isisn't divisible by 7.

5. Check whether the given numbers are divisible by ’11’ or not?

Solution:

To check for divisibility by 11, find the between the of the digits at odd places and the of the digits at even places.

If the difference is either or a of 11, the number is divisible by 11.

(a) 786764

Solution:

Divisible by 11: YesNo

(7 + 6 + 6) - (8 + 7 + 4) = - = .

(b) 536393

Solution:

Divisible by 11: YesNo

(5 + 6 + 9) - (3 + 3 + 3) = - = .

(c) 110011

Solution:

Divisible by 11: YesNo

(1 + 0 + 1) - (1 + 0 + 1) = - = .

(d) 1210121

Solution:

Divisible by 11: YesNo

(1 + 1 + 1 + 1) - (2 + 0 + 2) = - = .

(e) 758043

Solution:

Divisible by 1: YesNo

(7 + 8 + 4) - (5 + 0 + 3) = - = .

(f) 8338472

Solution:

Divisible by 11: NoYes

(8 + 3 + 4 + 2) - (3 + 8 + 7) = - = .

(g) 54678

Solution:

Divisible by 1: NoYes

(5 + 6 + 8) - (4 + 7) = - = .

(h) 13431

Solution:

Divisible by 11: YesNo

(1 + 4 + 1) - (3 + 3) = - = .

(i) 423423

Solution:

Divisible by 11: YesNo

(4 + 3 + 2) - (2 + 4 + 3) = - = .

(j) 168861

Solution:

Divisible by 11: YesNo

(1 + 8 + 6) - (6 + 8 + 1) = - = .

6. If a number is divisible by ‘8’, then it also divisible by ‘4’ also. Explain?

Solution: YesNo

A number is divisible by 8 if its last digits are divisible by 8.

Since 8 is a of 4 (8 = × 4), if a number is divisible by 8, it can be written as (where k is an integer).

This can also be written as 4 × .

Since 2k is an integer, the number is also a of 4, and therefore divisible by 4.

7. A 3-digit number 4A3 is added to another 3-digit number 984 to give a four-digit number 13B7, which is divisible by 11. Find (A + B).

Solution:

4A3 + 984 = 13B7

Considering the units place, + = .

Considering the tens place, A + = .

Considering the hundreds place, + = .

Since 13B7 is divisible by 11, (1 + ) - ( + 7) = 1 + B - = - must be a multiple of 11.

B - 9 can be 0 or 11 or -11, etc. Since B is a digit, it can only be 0 to 9.

If B - 9 = 0, B = . Then A + = , so A = .

If B - 9 = -11, B = (not possible)

If B - 9 = 11, B = (not possible)

So, A = 1 and B = 9. Therefore, A + B = + = .