LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

DIVISIBILITY

**DIVISIBILITY -**

**Divisibility means dividing a number leaving no remainder. Very precisely, when any dividend is divisible by any divisor but without any reminder is called dividend is perfectly divisible by divisor.**

**A number is said to be divisible
by the numbers that divide
it without leaving
a remainder.**

**There are many numbers which will be divisible by different different number, but the question is how to recognize the number which will be divisible by which number. There are some examples are given below for your better understanding which will help you to recognize that, which number is divisible by which number.**

**v. In this lesson we shall learn by which numbers
we can divide a given number without
dividing it.**

**v. Just seeing the number we will be able to say by which numbers we can divide the number.**

**v. Say a number
417540. It is a big number. I can say this number is divisible by 2, 3, 4, 5, 6, 10, 12 without doing any division. If you learn the rules you will also easily do it.**

**Isn’t it interesting .Yes, let’s learn about it.**

**§ RULES OF DIVISIBILITY -BY 2, 3, 4, 5, 6, 9, 10, 11, 12 -**

__DIVISIBILITY BY 2 :-__ A number is divisible
by 2 if its last digit (one’s place) is an even number
or zero (0,2,4,6,8).

**Examples are 540, 12, 84, 806, 1358, 24238.**

__DIVISIBILITY BY 5 :-__ A number is divisible by 5 if its last digit (one’s place) is either
zero or 5 (0 or 5).

**Examples are 45; 220; 102675; 320525**

__DIVISIBILITY BY 10 :-__ A number is divisible by 10 if its last digit (one’s
place) is zero.

**Examples are 780, 4700, 64890.**

__DIVISIBILITY BY 3 :-__ A number is divisible by 3 if the sum of the digits is divisible by 3.

**Examples are 243 (2+4+3=9) (The sum 9 is divisible
by 3.)**

**8136 (8+1+3+6=18) (The sum 18 is divisible
by 3.)**

__DIVISIBILITY BY 4 :-__ A number is divisible by 4 if the number formed by its last two digits is divisible
by 4 or if the last two digits are both zeroes.

**Examples are 2148 (Since, last 2 digits 48 is divisible
by 4; 48÷4=12) 7300
(Since, last two digits are 00)**

__DIVISIBILITY BY 11:-__ A number is divisible by 11 if the difference between the sum of the digits in the odd places and in the even places is either zero or divisible by 11.

**Example 1331 ; 86845**

**1331 = (1 + 3) [1st place + 3rd place] - (3 + 1) [2nd place + 4th place]**

** = 4 - 4 = 0**

**86845 = (8 + 8 + 5) [1st place + 3rd place + 5th place] - (6 + 4) [2nd place + 4th place]**

** = 21 - 10 = 11 (Divisible by 11)**

__DIVISIBILITY BY 12:-__ A number is divisible
by 12 if it is divisible by 3 and 4 both.

**Example: 5364 is divisible by 12. (5+3+6+4 = 18 which is divisible
by 3. 64 is divisible
by 4)**

__DIVISIBILITY BY 6:-__ A number is divisible by 6 if it is divisible by 3 and 2 both. It's last digit (one’s place) must be an even number and some of its digits must be divisible by 3.

**Example - 84, 264, 2142**

**84 => 8 + 4 = 12 (Divisible by 3)**

**264 => 2 + 4 + 6 = 12 (Divisible by 3)**

**2142 => 2 + 1 + 4 + 2 = 9 (Divisible by 3)**

__DIVISIBILITY BY 9:-__ A number is divisible by 9 if the some of its digits be divisible by 9 (just like 3).

**Example - 4158, 9846, 8464, 98325. **

**4158 => 4 + 1 + 5 + 8 = 18 (Divisible by 9)**

**9846 => 9 + 8 + 4 + 6 = 27 (Divisible by 9)**

**8464 => 8 + 4 + 6 + 4 = 22 (Not divisible by 9), So, 8464 is not divisible by 9.**

**98325 => 9 + 8 + 3 + 2 + 5 = 27 (Divisible by 9)**