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What is the divisibility rule of \[16\] and \[17\] ?

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Last updated date: 20th Jul 2024
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Answer
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Hint: To simplify this question , we need to solve it step by step . Here we are going to determine that what numbers can be divisible by \[16\]and \[17\] by just performing simple and short calculations , find out the set of numbers that the numbers \[16\] and \[17\]can divide completely ( i.e. there is no remainder left over ) by the number while dividing the function Using this , we are able to determine the number is divisible or not without performing actual division . From the rules of divisibility we of \[16\] and \[17\] we can easily determine all possible numbers divisible by them.

Complete step-by-step answer:
The requirements for a number to be divisible by \[16\] - We need to check the thousand’s digit first depending upon if it's even or odd .
If the thousands digit is even then the number formed by the last three digits must be divisible by 16. And If the thousands digit is odd then the number formed by the last three digits plus eight must be divisible by sixteen. We can understand it through an example -
For example, in \[654,320\]
Here , the thousands digit (4) is even and the last three digits is \[320\] which is divisible by \[16\].
So, the number \[654,320\] is divisible by \[16\].
Similarly ,
\[254,176:{\text{ }}176\]
the thousands digit (4) is even and the last three digits form 176 which is divisible by 16. So, the number \[254,176\] is divisible by \[16\].
\[254,176:{\text{ }}176\] is divisible by \[16\]
\[3408:{\text{ }}408 + 8 = 416\] which is divisible by \[16\]
In order to determine that the number is divisible by \[16\] , we need to follow the above steps .

For divisibility of \[17\] –
We need to subtract 5 times the last digit from the remaining truncated number. In other words , we can say , a number is divisible by 17 if you multiply the last digit by 5 and subtract that from the rest. If that result is divisible by 17, then your number is divisible by 17. You have to repeat the step as necessary. If the result is divisible by \[17\], the original number is also divisible by \[17\].
For example, \[986\] we can do :
\[98 - \left( {6{\text{ }} \times {\text{ }}5} \right) = {\text{ }}68\] .
Since 68 is divisible by 17, then 986 is also divisible by 17.
Check for\[2278::{\text{ }}227 - \left( {5 \times 8} \right) = 187\]. Since 187 is divisible by 17, the original number 2278 is also divisible.

Note: Last 4 digit should be divisible by 16 .. if number contains less than 4 digit then divide complete number by 16.
Always try to understand the mathematical statement carefully and keep things distinct .
Remember the properties and apply appropriately .
Choose the options wisely , it's better to break the question and then solve part by part .