Question
Using divisibility tests, determine which of the following numbers are divisible by $2;$ by $3;$ by $4;$ by $5;$ by $6;$ by $8;$ by $9;$ by $10;$ by $11 ($say, yes or no$):$
Number Divisible by
$2$ $3$ $4$ $5$ $6$ $8$ $9$ $10$ $11$
$128$                  
$990$                  
$1586$                  
$275$                  
$6686$                  
$639210$                  
$429714$                  
$2856$                  
$3060$                  
$406839$                  

Answer

 
Here, we have to divide the given set of numbers by the other set of given numbers to see whether each one of them is divisible or not.
To check this, we follow the divisibility rules as given below:
$i.\ $For divisible by $2$: Any number that has $0$,$2$,$4$,$6$, or $8$ in its one's place is divisible by $2$.
$ii.\ $For divisible by $3$: If the sum of all the digits of the number is multiple of $3$, then it is divisible by $3$.
$iii.\ $For divisible by $4$: Any number whose last two digits $($i.e. one's and ten's place digits$)$ are divisible by $4$ then, the number is divisible by $4$.
$iv.\ $For divisible by $5$: Any number that has $0$ or $5$ in its one's place is divisible by $5$.
$v.\ $For divisible by $6$: If a number a divisible by both $2$ and $3$, then it is divisible by $6$.
$vi.\ $For divisible by $8$: Any number whose last three digits are divisible by $8$ then, the number is divisible by $8$.
$vii.\ $For divisible by $9$: If the sum of all the digits of the number is multiple of $9$, then it is divisible by $9$.
$viii.\ $For divisible by $10$: Any number that has $0$ in its one's place is divisible by $10$.
So, after following these rules, we can see the results as are given below:
Number Divisible by
$2$ $3$ $4$ $5$ $6$ $8$ $9$ $10$ $11$
$990$ Yes Yes No Yes Yes No Yes Yes Yes
$1586$ Yes No No No No No No No No
$275$ No No No Yes No No No No Yes
$6689$ Yes No No No No No No No No
$639210$ Yes Yes No Yes Yes No No Yes Yes
$429714$ Yes Yes No No Yes No Yes No No
$2856$ Yes Yes Yes No Yes Yes No No No
$3060$ Yes Yes Yes Yes Yes No Yes Yes No
$406839$ No Yes No No No No No No No
 
 

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