Divisibility Tests for 7

Q.

Five digit numbers divisible by $3$ are formed using the digits $0,1,2,3,4,5,6,7$ without repetition. The number of such numbers are?

1. $936$

2. $480$

3. $600$

4. $216$

Q.

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

$39*43$

Q.

Replace ‘ * ’ by a digit to make the number 764*91 divisible by 11.

Q.

Test the divisibility of the following numbers by $2,3$ and $6$

$176$

Q. $67x$ is a three digit number where $x$ is the digit in its units place. Which of the followings could be the value of $x$ if $67x$ is divisible by 7?

1. 2
2. 9
3. 3
4. 4

Q. Find the number(s) which are divisible by 7.

1. 233
2. 167
3. 672
4. 595

Q. What is the least value that should be given to ${}^{\prime }{a}^{\prime }$ so that the number $653a47$ will be divisible by 11?
[2 marks]

1. 6
2. 2
3. 9
4. 1

Q. Pick the number that is not divisible by 7.

1. 98
2. 1036
3. 671
4. 623

Q. Which of the following numbers is divisible by 7?

1. 178
2. 671
3. 533
4. 623

Q. The divisibility rule of 7 states that if a number is divisible by 7 then the last digit doubled and subtracted from the remaining number should be 0 or divisible by ___.

Q. If we use the divisibility rule for 7, the number 9317 is not divisible by 7.

1. False
2. True