
Arundeep

DIVISIBILITY BY THIRTEEN : Osculator for 13 is 4 (See note). But this time our osculator is not negative (as in case of 7). It is 'onemore' osculator. So, the working will be different now. This can be seen in the following examples.Ex 1 : Is 143 divisible by 13 ? Soln : 14 3 : 14 + 3 x 4 = 26 Since 26 is divisible by 13, the number 143 is also divisible by 13. or, This working may further be simplified as Step I : 1 4 3 16 [4 x 3 (from 143) + 4 (from 143)] Step II: 1 4 3 26/16 [4 x 6 (from 16) +1 ( from 16) +1 ( from 143) = 26] As 26 is divisible by 13, the number is also divisible by 13. Note : The working of second method is also very systematic. At the same time it is more acceptable because it has less writing work. Ex 2: Check the divisibility of 24167 by 13. 2 4 1 6 7 26/6/20/34 [4x7 (from 24167) +6 ( from 24167)= 34] [4x4 (from 3 4) +3 (from 34) +1 (from 24167) = 20] [4x0 (from 20) +2 (from 20) +4 (from 24167) = 6] [4x6 (from 6) +2 (from 24167) = 26] Since 26 is divisible by 13 the number is also divisible by 13. Remark : Have you understood tbc working ? If Your answer is no, we suggest you to go through each step carefully. This is very simple and systematic calculation. Ex 3: Check the divisibility of 6944808 by 13. Soln : 6 9 4 4 8 0 8 39/18/12/41/19/32 4x8+0 = 32 4x2+3+8 = 19 4x9+1+4 = 41 4x1+4+4 = 12 4x2+1+9 = 18 4x8+1+6 = 39 Since 39 is divisible by 13, the given number is divisible by 13. Note : (1) This method is applicable for "onemore" osculator only. So we can't use this method in the case of 7. (2) This is a oneline method and you don't need to write the calculations during exams. These are given merely to make you understand well. 