Divisibility Rule for 11
If the last four digits of a number are divisible by 16, the number is divisible by 16. For example, in 79645856 as 5856 is divisible by 16, 79645856 is divisible by 16
Divisibility Rule for 16
Although for any power of 2 such as 2n, the simple formula is to check last n digits and if the number formed by just last n digits is divisible by 2n, entire number is divisible by 2n and hence for divisibility by 16, one should check last four digits. For example, in 4373408, as last four digits 3408 are divisible by 16, entire number is divisible by 16.
If this is complicated, one can also try the rule - if the thousands digit is even, take the last three digits, but if the thousands digit is odd, add 8 to the last three digits. Now with this 3-digit number, multiply hundreds digit by 4, then add to the last two digits. If the result is divisible by 16, the entire number is divisible by 16.
Divisibility Rule for 17
Divisibility rules for somewhat larger primes are not of much help and many times they get complicated. Nevertheless, rules have been designed and for 17 one is, subtract 5 times the last digit from the rest.
For example in the number 431443, subtract 3×5=15 from 43144 and we get 43129 and as it is divisible by 17, number 431443 is also divisible by 17.
One can also perform series of such action. In above example to check whether 43129 is divisible by 17 or not, subtract 9×5=45 from 4312 and we get 4267 and to check for this, subtract 7×5=35 from 426 and we get 391 and finally 1×5=5 from 39 to get 34, which is divisible 17 and
hence 431443, 43129, 4267 and 391 all are divisible by 17
