Question 1: Using the test of divisibility, find which of the following numbers are divisible by 3?

(i) (ii) (iii) (iv) (v) (vi)

Answer:

Note: A number is divisible by , if the sum of the digits of the number is divisible by .

(i)

Sum of is divisible by . Hence is divisible by .

(ii)

Sum of is divisible by . Hence is divisible by .

(iii)

Sum of . is not divisible by . Hence is divisible by .

(iv)

Sum of . is divisible by . Hence is divisible by .

(v)

Sum of . is divisible by . Hence is divisible by .

(vi)

Sum of . is divisible by . Hence is divisible by .

Which of the above numbers are divisible by 9?

Note: A number is divisible by if the sum of the digits of the number is divisible by .

Therefore, and are divisible by .

Question 2: Using the test of divisibility, find which of the following numbers are divisible by 3?

(i) (ii) (iii) (iv) (v) (vi)

Which of the above numbers are divisible by 6?

Answer:

*Note: A number is divisible by , if the sum of the digits of the number is divisible by .**Note: A number is divisible by , if the last digit of the number is , and .**Note: A number is divisible by , if it is divisible both by and .*

(i)

Sum of . 26 $ is not divisible by . Hence is not divisible by . It is divisible by .

(ii)

Sum of is divisible both by and . Hence the number is also divisible by .

(iii)

Sum of is divisible by but not by . Hence the number is not divisible by .

(iv)

Sum of is divisible by but not by . Hence the number is not divisible by .

(v)

Sum of is divisible by and . Hence the number is also divisible by .

(vi)

Sum of is divisible by but not by . Hence the number is not divisible by .

Question 3: Using the test of divisibility, find which of the following numbers are divisible by ?

(i) (ii) (iii) (iv) (v) (vi)

Which of the above numbers are divisible by ?

Answer:

Note:

- A number is divisible by if the number formed by the last two digits of the number is divisible by .
- A number is divisible by if the number formed by then last three digits of the number is divisible by

(i)

is not divisible by . Hence the is not divisible by .

is not divisible by . Hence the is not divisible by .

(ii)

is not divisible by . Hence the is not divisible by .

is not divisible by . Hence the is not divisible by .

(iii)

is divisible by . Hence the is divisible by .

is divisible by . Hence the is divisible by .

(iv)

is not divisible by . Hence the is not divisible by .

is not divisible by . Hence the is not divisible by .

(v)

is divisible by . Hence the is divisible by .

is divisible by . Hence the is divisible by .

(vi)

is divisible by . Hence the is divisible by .

is divisible by . Hence the is divisible by .

Question 4: Which of the above numbers are divisible by 6?

(i) (ii) (iii) (iv) (v) (vi)

Answer:

*Note:*

*A number is divisible by , if the sum of the digits of the number is divisible by .**A number is divisible by , if the last digit of the number is , and .**A number is divisible by , if it is divisible both by and .*

(i)

Sum of is divisible by . Hence is divisible by .

The last digit is which is not divisible by .

Hence the number is not divisible by .

(ii)

Sum of is divisible by . Hence is divisible by .

The last digit is which is divisible by .

Hence the number is divisible by .

(iii)

Sum of is divisible by . Hence is divisible by .

The last digit is which is divisible by .

Hence the number is divisible by .

(iv)

Sum of is divisible by . Hence is divisible by .

The last digit is which is divisible by .

Hence the number is divisible by .

(v)

Sum of is divisible by . Hence is divisible by .

The last digit is which is not divisible by .

Hence the number is not divisible by .

(vi)

Sum of is not divisible by . Hence is divisible by .

The last digit is which is not divisible by .

Hence the number is not divisible by .

Question 5: Which of the above numbers are divisible by ?

(i) (ii) (iii) (iv) (v) v(i)

Answer:

*Note: A number is divisible by id the difference between the sum of its digits at odd places and the sum of the digits at even places is either 0 or a number divisible by .*

(i)

Difference = (sum of digits at odd places) – (sum of digits at even places) .

is not divisible by . Hence then number is not divisible by .

(ii)

Difference = (sum of digits at odd places) – (sum of digits at even places) .

is not divisible by . Hence then number is not divisible by .

(iii)

Difference = (sum of digits at odd places) – (sum of digits at even places)

is divisible by . Hence then number is divisible by .

(iv)

Difference = (sum of digits at odd places) – (sum of digits at even places)

is no divisible by . Hence then number is not divisible by .

(v)

Difference = (sum of digits at odd places) – (sum of digits at even places)

Hence then number is divisible by .

(vi)

Difference = (sum of digits at odd places) – (sum of digits at even places)

Hence then number is divisible by .

Thank you,

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