Finding the Unknown Digit if a Number is Divisible by another Number

Q.

Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by $3$:

1. $\_\_6724$

2. $4765\_\_2$

Q.

Write five pairs of prime numbers below $20$ whose sum is divisible by $5$?

Q.

Fill in the blanks with the smallest digit to make the number divisible by $9$:

$93\_\_\_07$

Q.

In the following replace * by the smallest number so that the given number is divisible by the number mentioned:
$4347*$ by $4$.

Q.

Fill in the blanks with the smallest digit to make the number divisible by $3$:

$47\_\_\_93$

Q.

Circle the numbers which are divisible by $2$.

$4263851629713582875030$

Q.

Using divisibility tests, write yes or no :

$12159$ is divisible by $2.$

Q. Charlie wants to buy a new house but he wants a house number that is divisible by both 4 and 5. Houses for sale are numbered 100 to 150. Which of these houses would he want to buy?

1. 110, 120 or 130
2. 120, 140 or 150
3. 100, 120 or 140
4. 130, 140 or 150

Q. $48$_$8$ is divisible by $8$. What are the possible whole numbers that can fill the blank?

1. 0, 8 and 9
2. 1, 4 and 8
3. 0, 4 and 8
4. 2, 4 and 8

Q. Consider the smallest five digit number $\text{\_6789}$. Guess the digit that can fit in the blank space, if the number is divisible by 9 in one case and 3 in the other case.

1. 6 and 0, respectively.
2. 3 and 6, respectively.
3. 6 and 3, respectively.
4. None of the above.

Q.

Test the divisibility of the following numbers by $7$.

$300630$

Q.

Fill in the blank with smallest digit to make ……….$70312$ divisible by $4$.

Q. Arrange the digits of the four-digit number $6014$ such that it is the smallest possible number divisible by $8.$

Q.

Test the divisibility of the following numbers by $7$.

$94563$

Q. Find the digits $xy$ such that the number $47xy$ is divisible by $30.$

1. $xy=30$
2. $xy=20$
3. $xy=50$
4. $xy=80$

Q.

$56780$

1. True
2. False

Q. The 4-digit number $7x86$ is evenly divisible by 9 and other 4-digit number $7y86$ is evenly divisible by 3.
Which of the following are smallest values of $x\&y?$

1. $x=6\&y=3$
2. $x=3\&y=0$
3. $x=6\&y=0$

Q. The smallest four digit number $\text{7\_86}$ is

Case I: exactly divisible by 9.

The digit that fits in the blank space is .

Case II: exactly divisible by 3.

The digit that fits in the blank space is .

Q. Mateo was listing out the numbers which are divisible by $12.$
In a particular number $9864$, he mistakenly fed $6$ in the tens place. Find the appropriate smallest digit.

1. 9
2. 6
3. 0
4. (b) and (c) above.

Q. Identify the digit $d$ such that the number $741d$ is divisible by $6.$

1. 0
2. 4
3. 6
4. 8