
Quick Divisibility – Part 1
Hello, this time I will discuss about Quick divisibility tests which will be useful in finding the factors of a number. This is very handy when solving questions involving L.C.M and G.C.F of numbers .
Checking whether a number is exactly divisible by 7, 13 ,19 ,23, 27,29,31 is difficult by using multiplication table . Quick divisibility tests, sequentially starting from 2, are discussed below. This saves a lot of time while finding factors.
1. Test for 2 – If unit digit is 0,2,4,6,8 2 the number is divisible by 2 . (even numbers )
2. TEST for 3 – If the sum of digits of a number is divisible by 3. EX- 12345, sum of digits is 1+2+3+4+5 = 15 , which is divisible by 5 . So the number 12345 is divisible by 3 .
3 . Test for 4 – If the number formed by last 2 digits is divisible by 4 . EX- 123456 , the number formed by the last 2 digits is 56 , which is divisible by 4 . So 123456 is divisible by 4
4 .Test for 5 – Unit digit is 5 or 0 .
5.Test for 6 – If it is divisible by both 2&3 .( Number is even and sum of digits is divisible by 3)
6. Test for 7 –
(1) 3 digit number – Multiply the unit digit by 2 and subtract it from the rest . If the result is divisible by 7, whole number is divisible by 7 . Ex- 945 , unit digit is 5 and rest is 94 , 94 – 2×5 = 84 , which is divisible by7 , So 945 is divisible by 7 .
(2) For numbers having minimum of 4 digits – If q is number formed by last 3 digits and p is number made up of rest of the numbers , then if ( p-q ) is divisible by 7 , then the whole number is divisible by 7 .
Four digit number – 9331 ,q= number formed by last 3 digits = 331 , p = rest of the numbers = 9 p – q = 9 – 331 = – 322 ,which is divisible by 7 Hence 9331 is divisible by 7 .
Five digit number – 34426 , p=34 , q =426 , p – q = 426 – 34 = 392 which is divisible by 7 ( since it is now a 3 digit number you can test it as discussed above , 39 – 2×2=35, divisible by 7 ) Hence 34426 is divisible by 7 .
Six digit number – 976213 , p = 976 , q = 213 , p – q = 976 -213 = 763 which is divisible by 7 . So the number 976231 is divisible by 7 .
To be Continued.



the Kintamani Volcano, an active volcano that was said to have erupted some two years back. What a moment when we sat in a restaurant there, facing the volcanic mountains with their open peaks and wondering about the beauty and the fury of nature, the cool breeze, being a welcome surprise. The day ended in a coffee plantation where we were taken through the process of making the world famous and the most expensive Luwak Coffee, made with coffee beans procured from the faeces of a mongoose like Asian animal, amazing isn’t it! Though I didn’t want to taste some. The trip ended with a visit to the ruins of a Buddhist monastery the Goa Gajah Cave built around the tenth century.
The excitement of the next day was evident in all of us when we heard we were heading towards the Tanah Lot Temple, built on a low jutting cliff over the huge, blue Indian Ocean. The view of the temple with its unique Balinese architecture and the blue waves with their white frothy crown lashing against the shore was definitely a photographer’s or an artist’s dream destination. One could wade into the sea and see the temple at close quarters. The cool waters of the sea brushed aside the afternoon heat. We now headed towards our much awaited trip on a cruise, the Sunset Dinner Cruise, where we were treated with some delicious food and some traditional Balinese dance performances…. Couldn’t ask for more!
The famous Ulluwatu Temple was our destination on the fourth day. Two temples built on two tall cliffs facing the tremendous ocean. The various shades of blue and green were so evident in the waters which were definitely not calm, rather quite dangerous, held us glued to one spot. The beauty and the awe of the place yet the calmness and the serenity of the temples made the place seemed almost heavenly. We also enjoyed some amazing sea rides at the Benoa Beach from where we went to the Turtle Island and held and feed turtles and also had the weird yet unimaginable experience of holding a python…. with its scaly muscular movement and its awesome size and length.


