Answer

Verified

348.9k+ views

**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 .

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE