DIVISIBILITY QUIZ - FOR 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 AND PRIME DIVISORS 13 TO 47 AND ABOVE

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Please study
Multiplication Tables
and
Division before Divisibility Quiz
They are prerequisites here.

Here we study methods that can be used to determine
whether a number is evenly divisible by other numbers.

These are shortcuts for testing a number's factors
without resorting to division calculations.

The rules given below transform a given number's divisibility
by a divisor to a smaller number's divisibility by the same divisor.

If the result is not obvious after applying it once,
the rule should be applied again to the smaller number.

We present the rules with examples, in a simple way,
to follow, understand and apply.

We provide the rules for all the single digit divisors
and prime divisors upto 47 and above
and a general method which is simple to use.

Divisibility Rule for 2 : Divisibility Quiz

A number is divisible by 2, if its last digit (units' digit) is divisible by 2.
i. e. if its last digit (units' digit) is any of the digits
0, 2, 4, 6 and 8 ( i. e. Even digits ).
i. e. All EVEN NUMBERS are divisible by 2.

Examples:

112 has last digit as 2 (even) and so is divisible by 2.
121 is not divisible by 2, since last digit is 1 (odd).

1234 is divisible by 2, since the last digit is 4 (even).
3003 is not divisible by 2, since last digit is 3 (odd).

95030 is divisible by 2, since the last digit is 0 (even).
68735 is not divisible by 2, since last digit is 5 (odd).

345617 is not divisible by 2, since last digit is 7 (odd).
231276 is divisible by 2, since the last digit is 6 (even).

1235678 is divisible by 2, since the last digit is 8 (even).
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Divisibility Rule for 4 : Divisibility Quiz

A number is divisible by 4, if the number formed by its last two digits
( i. e. tens' digit and units' digit) is divisible by 4.

Note : If the number is odd, there is no need to check the rule,
as odd number is not divisible by even number (4).

Example 1 of Divisibility Quiz for 4

Find whether 4025 is divisible by 4 or not.

Solution :
As the number, 4025 is odd, it is not divisible by 4. Ans.

Example 2 of Divisibility Quiz

Find whether 234 is divisible by 4 or not.

Solution :
We verify whether the number formed by the last two digits (34)
is divisible by 4 or not.


              Dividend
 Divisor   4 )   34   ( 8   Quotient    
                 32
                 ---
                  2   Remainder 
                 ---  

As the remainder is not zero, 34 is not divisible by 4.
Hence 234 is not divisible by 4. Ans.

Example 3 of Divisibility Rule for 4

Find whether 5678 is divisible by 4 or not.

Solution :
We verify whether the number formed by the last two digits (78)
is divisible by 4 or not.


              Dividend
 Divisor   4 )   78   ( 19   Quotient    
                 4
                 ---
                 38
                 36    
                 ---  
                  2   Remainder 
                 ---   

As the remainder is not zero, 78 is not divisible by 4.
Hence 5678 is not divisible by 4. Ans.

Example 4 of Divisibility Quiz

Find whether 81756 is divisible by 4 or not.

Solution :
We verify whether the number formed by the last two digits (56)
is divisible by 4 or not.


              Dividend
 Divisor   4 )   56   ( 14   Quotient    
                 4
                 ---
                 16
                 16    
                 ---  
                  0   Remainder 
                 ---   

As the remainder is zero, 56 is divisible by 4.
Hence 81756 is divisible by 4. Ans.

Example 5 of Divisibility Rule for 4

Find whether 987432 is divisible by 4 or not.

Solution :
We verify whether the number formed by the last two digits (32)
is divisible by 4 or not.


              Dividend
 Divisor   4 )   32   ( 8   Quotient    
                 32
                 ---
                  0   Remainder 
                 ---  

As the remainder is zero, 32 is divisible by 4.
Hence 987432 is divisible by 4. Ans.

Thus we can check divisible by 4 of any number,
how big it may be, by simply checking the
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Divisibility Quiz for 3, 5, 6, 7, 8, 9, 10, 11,
Prime Divisors up to 47 and above.

Given below are the Links for
Divisibility Quiz for 3, 5, 6, 7, 8, 9, 10, 11
and Divisibility Quiz for any Prime Divisor.

Divisibility by 3 and 6

Divisibility by 5, 9 and 10

Divisibility by 7

Divisibility by 8

Divisibility by 11

Divisibility Test for 2 to 11

Divisibility by Prime Divisor

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