Q. 13.7( 16 Votes )

Without actual division, using divisibility rules, classify the following numbers as divisible by 3, 4, 5, 11.

803, 845, 474, 583, 1067, 350, 657, 684, 2187, 4334, 1905, 2548.

Answer :

An integer ‘a’ is divisible by 3 if and only if the sum of the digits of ‘a’ are divisible by 3.


A number ‘a’ (having more than one digit) is divisible by 4 if and only if the 2-digit number formed by the last two digits of ‘a’ are divisible by 4.


An integer ‘a’ is divisible by 5 if and only if it ends with 0 or 5.


The number is divisible by 11 if and only if the difference between the sum of the digits in the odd place and the sum of the digits in the even place is divisible by 11.


Using these divisibility test we can find out which number is divisible by 3, 4, 5 and 11 without actually dividing


1) 803 – the sum of the digit at an odd place that is 8+3 = 11 and the sum of the digit at even place that is 0 and their difference = 11- 0 = 11 is divisible by 11 so the number is divisible by 11


2) 845- since the last digit is 5, the number is divisible by 5


3) 474 – since the sum of the digits 4 +7 +4 = 15 is divisible by 3, the number is divisible by 3


4) 583 - The sum of the digit at an odd place that is 5+3 = 8 and the sum of the digit at even place that is 8 and their difference = 8 – 8 = 0 is divisible by 11 so the number is divisible by 11


5) 1067 - The sum of the digit at an odd place that is 7+0 = 7 and the sum of the digit at even place that is 1 +6 = 7 and their difference = 7 - 7 = 0 is divisible by 11 so the number is divisible by 11


6) 350 - Since the last digit is 0, the number is divisible by 5


7) 657 - Since the sum of the digits 6 +5 +7 = 18 is divisible by 3, the number is divisible by 3


8) 684- since the last two digit that is 84 of the number is divisible by 4, the number is divisible by 4


9) 2187 - since the sum of the digits 2+1 +8 +7 = 18 is divisible by 3, the number is divisible by 3


10) 4334 - the sum of the digit at an odd place that is 4+3 = 7 and the sum of the digit at even place that is 3+4 = 7 and their difference = 7 - 7 = 0 is divisible by 11 so the number is divisible by 11


11) 1905 - since the last digit of the number is 5, the number is divisible by 5


12) 2548 - since the last two digit that is 48 of the number is divisible by 4, the number is divisible by 4


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