Divisibility Tests for 11

Q.

$18$ is divisible by both $2$ and $3.$. It is also divisible by $2x3=6.$ Similarly, a number is divisble by $4$ and $6$. Can we say that the number must be divisible by $4x6=24?$ If not, give an example to justify your answer.

Q.

Question 36
Which of the following numbers is divisible by 11?

(A) 1011011
(B) 1111111
(C) 22222222
(D) 3333333

Q.

A number is divisible by $11$ if the difference between the sum of digits at its odd places and that of digits at the even places is either $0$ or divisible by ……...

Q.

If a number is divisible by $9$ and $10$ both, then it must be divisible by $90$. (True or False)

1. True
2. False

Q.

Is $10824$ divisible by $11$?

Q.

The Number $31,13,11,31,13,11,31,13,11,311$ Is Divisible By both $3$ And $11$. (True / False)

1. True
2. False

Q.

Check the divisibility of 61809 by 11.

Q.

A number is divisible by $15$. By what other numbers will that number be divisible?

Q.

Check the divisibility of 1331 by 11.

Q.

Find the smallest digit that should be replaced at $*$ place in the number $1723*4$ so that the number is divisible by $11$.

Q.

$1x35$ is divisible by $9$ if $x$ $=$ _______.

Q.

Which of the following numbers is divisible by 11?

1. 10000001, 459756

2. 4568947, 97455

3. 9000001, 45975

4. 4569874, 547952

Q.

$20x3$ is a multiple of $3$ if the digit $x$ is ______ or ______ or ______.

Q.

If a $3$-digit number $\mathrm{abc}$ is divisible by $11$, then ______ is either $0$ or multiple of $11$.

Q.

If a number 3A98 is divisible by 11. Then find the value of A? [4 MARKS]

Q.

39M2 , What should be the least value of M so that it is divisible by 11 ?

1. 8

2. 9

3. 17

4. 22

Q.

Using the divisibility test, determine $17852$ is divisible by $6$ or not?

Q.

Question 148

Fill in the blank to make the statement true.

If the difference between the sum of digits at odd places (from the right) and the sum of digits at even places (from the right) of a number is either 0 or divisible by ___, then the number is divisible by 11.

Q.

$1x35$ is divisible by $9$ if $x$ $=$ _______.

Q.

Using the divisibility test, determine $1258$ is divisible by $6$ or not?

Q.

Question 5 (a)

Write the smallest digit and the largest digit in the blank space for the given number so that the number formed is divisibly by 3:
________6724

Q. Find the sum of smallest three digit even number and greatest three-digit odd number using the digits $6,2,3$

1. $859$
2. $958$
3. $598$
4. $985$

Q. Which one of the following numbers is exactly divisible by $11$?

1. $235641$
2. $245642$
3. $315624$
4. $415624$

Q.

Find the remainder without performing actual division when 45969 is divided by 11.

1. 6

2. 7

3. 8

4. 0

Q.

Using the divisibility test, determine $12583$ is divisible by $6$ or not?

Q. The sum of three consecutive multiples of $11$ is $363$. find multiples.

Q.

If a number $a$ is divisible by $b$, then it must be divisible by each factor of $b$. State whether the statement given is true or false

1. True
2. False

Q. Which of the following number is divisible by 3?

1. 12346
2. 12347
3. 12349
4. 12351

Q.

A three-digit number $abc$ is divisible by $6$ if $c$ is an even number and $a+b+c$ is a multiple of $3$. State whether the statement given is true (T) or false (F).

1. True
2. False

Q.

624 is completely divisible by:

1. 3

2. 4

3. 6

4. 9