** **

1. Test for 19 – Multiply unit digit by 2 Add to the remaining. Ex – 65341 , unit digit is 1 and rest is 6534 6534 +1×2= 6536 , ( Repeat the same process again and again ) 653 + 2×6 = 665 , 66 + 2×5 = 76 , divisible by 19 . So, 65341 is divisible by 19

2. Test for 23 – Multiply unit digit by 7 and add to the remaining. Ex – 15019 , unit digit is 9 and rest is 1501 1501+ 9×7 = 1501+63 =1564 , Again 156+4×7 = 156+28 = 184 , 18+4×7 =46 is divisible by 23 . So, 15019 is divisible by 23.

3. Test for 27 – (1) For 3 digit number — Multiply the 1st digit by 8 , subtract it from rest . Ex – 675 , 75 – 6×8 = 75 – 48 =27 which is divisible by 27 . So 675 is divisible by 27 ( 2 ) Digits more than 3 – If last 3 digits is “b” and rest is “ a “ , a+b is divisible by 27 then the whole number is divisible by 27 . Ex– In 12312 , b =312, a=12 , a+b = 312+12=324 which is divisible by 27 So the number 12312 is divisible by 27

4. Test for 29 – Multiply unit digit by 3 and add to the remaining. Ex – 10324 , unit digit is 4 and remaining is 1032 1032 + 3×4 =1044 , ( repeat the same again and again ) 104+3×4 =116 , 11+3×6=29 , which is divisible by 29 . So, 10324 is divisible by 29

Kiran Bala Dash (Grandmother of Tanay – 4E and Vinay – LKG D).

Retired Lecturer in Mathematics

** **