Divisibility Tests for 4

Q.

Show that ${\mathrm{n}}^2-1$is divisible by $8$, if $\mathrm{n}$ is an odd positive integer.

Q.

In the following numbers, replace * by the smallest number to make it divisible by $3$

$53*46$

Q.

Using divisibility tests determine $572$ is divisible by $4$ and divisible by $8$:

Q.

Question 3(d)

Find the value of the following:

$3845\times 5\times 782+769\times 25\times 218$

Q. Using divisibility tests, determine which of the following numbers are divisible by 5 and 10.
i) 639210
ii) 17852

Q.

Find all the numbers between $20$ and $40$ that are divisible by:

(a) $2$

Q. What is the largest $3$ digit number exactly divisible by $4$?

1. $124$
2. $846$
3. $984$
4. $996$

Q.

Using divisibility tests, determine the given number $71,124$ is divisible by $6$.

Q.

All numbers which are divisible by 4 must also be divisible by 8. (True or False)

1. True
2. False

Q.

Check the divisibility of the following number by $4$:

$986219$

Q. Using divisibility test, determine whether the given number is divisible by 6: 297144
[3 marks]

Q.

The number with four or more digits is exactly divisible by $8,$ if the number formed by its last two digits ( i.e, ones and tens ) is exactly divisible by $8.$

1. True
2. False

Q. Using divisibility test, determine whether the given number is divisible by 4 and by 8: 5500​

Q.

In each of the following numbers, replace $*$ by the smallest number to make it divisible by $3$

$27*4$

Q.

In each of the following numbers, replace $*$ by a digit to make the number divisible by $11$.

$9*8071$

Q.

The sum of two consecutive odd numbers is divisible by 4. Verify this statement with the help of some examples.

Q.

Classify the set $A=\left\{m:misamonthoftheyearandmhas29daysinaleapyear\right\}$ as singleton or empty set.

Q.

Using divisibility tests, determine the given number $78,651$ is divisible by $6$.

Q. Using divisibility tests, determine which of the following numbers are divisible by 5 and 10.
i) 639210
ii) 17852

Q. A number is divisible by 4 if the number formed by units and tens places is divisible by 4

1. True
2. False

Q. In the natural numbers from $10$ to $250$, how many are divisible by $4$?

Q. Multiply 354 and 111 and find the sum of first three digits of the result.

1. 22
2. 21
3. 14
4. 18

Q. Check whether $2^2+2^3+2^4$ is divisible by $2$ or $4$ or by both $2$ and $4$?

Q. Fill in the blanks
The smallest digit by which $\ast$ should be replaced in $5095\ast 6$, so that it is divisible by $4$ is _____.

Q. If the last two digits of a number is divisible by $4$, the number is also divisible by ____.

1. $4$
2. $5$
3. $7$
4. $9$

Q.

Determine whether $10824$ is divisible by $11$

Q.

how is 901153 divisible by 11?

Q. Use 'Divisibility Rules' to determine which one of the following numbers is divisible by 4.

1. 5304
2. 5386
3. 5014
4. 6318

Q. Check whether the given numbers are divisible by $4$ or not ?
(a) $3024$ (b) $1000$ (c) $412$ (d) $56240$

Q. Which of these is the odd one out?
$2012,2010,2008,2004$.