BLOG 3 PLAYING WITH NUMBERS -DIVISIBILITY TESTS - a recall

BLOG 3 PLAYING WITH NUMBERS -DIVISIBILITY TESTS - a recall

    GOOD MORNING BOYS ,

LEARNING OUTCOMES  FOR TODAY' S LESSON 

By the end of this lesson you will be able to RECALL the divisibility tests for 2,3,4,5,6,8 and 10 and hence apply it in later session to solve simple puzzles. 


  

Divisibility Test  OR SHORTCUTS 

As the name suggests, divisibility tests or division rules in Maths help one to check whether a number is divisible by another number without actual division. If a number is completely divisible by another number it means that in such a case quotient will be a whole number and the division will leave zero as remainder.

Divisibility by 2

Any even number or number whose last digit is an even number i.e.  2,4,6,8 including 0 is always completely divisible by 2.

Example: 508 is an even number and divisible by 2 but 509 is not an even number, hence not divisible by 2. Procedure to check whether 508 is divisible by 2 or not is as follows:

• Consider the number 508
• Just take the last digit 8 and divide it by 2
• If the last digit 8 is divisible by 2 then the number 508 is also divisible by 2.

                                           Divisibility Rules for 3                                           

CLICK ON THIS LINK TO KNOW ABOUT THE DIVISIBILITY TEST OF 3 AND 9

Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3 i.e., it is a multiple of 3

Consider a number, 308. 

To check whether 308 is divisible by 3 or not, take sum of the digits (i.e. 3+0+8= 11). 

Now check whether the sum is divisible by 3 or not. 

If the sum is a multiple of 3 then the original number is also divisible by 3. 

Here, since 11 is not divisible by 3, 308 is also not divisible by 3.

Similarly, 516 is divisible by 3 completely as the sum of its digits i.e. 5+1+6=12, is a multiple of 3.

                                                  Divisibility by 9                                            

The rule for divisibility by 9 is similar to divisibility rule for 3. That is, if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

Example: Consider 78532, as the sum of its digits (7+8+5+3+2) is 25, which is not divisible by 9, hence 78532 is not divisible by 9

   

WATCH THE VIDEO TO SEE THE DIVISIBILITY TESTS FOR 2,3,4,5,6,9

                                                   Divisibility by 4                                           

If the last two digits of a number are divisible by 4, then that number is a multiple of 4 and is divisible by 4 completely.

Example: Take the number 2308. Consider the last two digits i.e.  08. As 08 is divisible by 4, the original number 2308 is also divisible by 4.

                                                       Divisibility by 5                                           

Numbers with last digit 0 or 5 are always divisible by 5.

Example: 10, 10000, 10000005, 595, 396524850 etc.

                                                      Divisibility by 6                                              

Numbers which are divisible by both 2 and 3 are divisible by 6. That is, if last digit of the given number is even and the sum of its digits is a multiple of 3, then the given number is also a multiple of 6.

Example: 630, the number is divisible by 2 as the last digit is 0.

The sum of digits is 6+3+0 = 9, which is also divisible by 3.

Hence 630 is divisible by 6.

                                                    Divisibility by 8                                               

If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.

Example: Take number 24344. Consider the last two digits i.e.  344. As 344 is divisible by 8, the original number 24344 is also divisible by 8.

                                                     Divisibility by 10                                            

Divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.

Example: 10, 20,30,1000,5000,60000 etc.

Divisibility Rules Solved Examples

Example 1:

Check if 288 is divisible by 2.

Solution:

Given, 288 is a number.

If the last digit of 288 is divisible by 2, then 288 is also divisible by 2.

The last digit of 288 is 8, which is divisible by 2, such that;

8/2 = 4

Hence, 288 satisfy the divisibility rule for 2.

Example 2:

Check is 195 is divisible by 4 or not.

Solution:

As we can see, the last digit of 195 is 5, which is not divisible by 4.

Hence, 195 is not divisible by 4.

Example 3:

Check is 15287 is divisible by 3 or not

Solution:

As we can see, the sum of the  digits is  1+ 5+2 + 8 + 7 = 23, which is not divisible by 3.

Hence, 195 is not divisible by 3.

Example 4:

Check is 152875 is divisible by 9 or not

Solution:

As we can see, the sum of the  digits is  1+ 5+2 + 8 + 7+5 = 28, which is not divisible by 9.

Hence, 195 is not divisible by 9.

Example 5:

Check is 15287 is divisible by 6 or not

Solution:

As we can see, the sum of the  digits is  1+ 5+2 + 8 + 7 = 23, which is not divisible by 3.

Hence, 15287 is not divisible by 6 

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