--INTRODUCTION-- Let us observe the situation. Hasini wants to distribute chocolates to her classmates on her birthday. Her father brought a box of 125 chocolates. There are 25 students in her class. She decided to distribute all the chocolates such that each one would get equal number of chocolates. First, she thought of giving 2 chocolates each but found that some chocolates were remaining. Then again she tried of giving 3 each, but again some chocolates were remaining. Finally, she thought of giving 5 chocolates each. Now, she found that no chocolates were remaining. Is there a way of coming directly to the answer? Think. Of course she can divide 125 by 25 ---DIVISIBILITY RULE--- The process of checking whether a number is divisible by a given number or not without actual division is called divisibility rule for that number. ---Divisibility by 2--- a number is divisible by 2 if it has any of the digits 0,2,4,6 or 8 in it's ones place Are 953, 9534, 900, 452 divisibile by 2? Also check by actual division. ---Divisibility by 3--- if the sum of the digits is a multiple of 3, then the number is divisible by 3. Let us now add the digits of 21, 36, 54, 63, 72, 117 2 + 1 = 3 5 + 4 = ______ 7 + 2 = ______ 3 + 6 = _____ 6 + 3 = ______ 1 + 1 + 7 = ______ All these sums are divisible by 3. Check whether the following numbers are divisible by 3? i. 45986 ii. 36129 iii. 7874 ---Divisibility by 6--- If a number is divisible by both 2 and 3 then it is also divisible by 6. 1. Is 7224 divisible by 6? Why? 2. Give two examples of 4 digit numbers which are divisible by 6. 3. Can you give an example of a number which is divisible by 6 but not by 2 and 3. Why? ---Divisibility by 9--- A number is divisible by 9, if the sum of the digits of the number is divisible by 9 we take 81, 8 + 1 = 9 similarly 99, 9 + 9 = 18 divisible by 9 1. Test whether 9846 is divisible by 9? 2. Without actual division, find whether 8998794 is divisible by 9? 3. Check whether 786 is divisible by both 3 and 9? ---Divisibility by 5--- A number is divisible by 5 if its units place is 0 or 5. Are all the numbers 20, 25, 30, 35, 40, 45, 50 divisible by 5? ---Divisibility by 10--- A number is divisible by 10 if it has zero (0) in its units place. All of them are divisible by both 5 and 2. 110, 200, 360, 490, 1190, 1510 here all these number is divisible by 10 because their units place is 0. ---Divisibility by 4--- A number is divisible by 4, if the number formed by its last two digits (i.e. tens and ones) is divisible by 4. TEXTBOOK TABLE Pg=43 1. Is 100000 divisible by 4? Why? 2. Give an example of a 2 digit number that is divisible by 2 but not divisible by 4? ---Divisibility by 8--- A number with 4 or more digits is divisible by 8, if the number formed by its last three digits is divisible by 8. The divisibility for numbers with 1, 2 or 3 digits by 8 has to be checked by actual division. Verify whether 93624 is divisible by 8? 93624 = 90000 + 3000 + 600 + 20 + 4 We know that 1000 is divisible by 8. Here, 90000 and 3000 are multiples of 1000, they are certainly divisible by 8. So, it is enough to test the divisibility of the last three digits of the number. Is 624 divisible by 8? yes. Hence, the given number 93624 is also divisible by 8 Test whether the following numbers are divisible by 8? i. 9774 ii. 5,31,048 iii. 5500 --- Divisibility Rule for 11--- A given number is divisible by 11, if the difference between the sum of the digits at odd places and the sum of the digits at even places (from the right) is either 0 or divisible by 11. Is 6535 divisible by 11? Sum of the digits at odd places = 5 + 5 = 10 Sum of the digits at even places = 3 + 6 = 9 Their difference = 10 - 9 = 1 Is 1 divisible by 11? No So, 6535 is not divisible by 11. Check whether the following numbers are divisible by 11? i. 859484 ii. 10824 iii. 20801