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.
