Answer
437.4k+ views
Hint:First we need to find the smallest digit and greatest digit in the given number so that it is formed and it is divisible by \[3\].Also we need to know the definition of divisibility test of $3$.A number is divisible by $3$ if the sum of its digits is divisible by $3$.Using this rule and doing some calculations on it Finally we will get the required digits.
Complete step-by-step answer:
It is given that the given number is $\_6724$
We have to find the blank space at smallest and greatest digit and it is divisible by \[3\]
A number is divisible by \[3\] if the sum of its digits is divisible by\[3\].
Now we have to sum of digits in the given number =$\_ + 6 + 7 + 2 + 4 = \_ + 19$
Then we need to check numbers for blank space to give sum would be divisible by 3
We can see here on simplifications the digits which when added them in the result $\left( {19} \right)$ gives the final number will divisible by $3$
Hence we got the smallest digit will be $2$ which will be of the form \[26724\] and we got the greatest digit will be $8$ which will be of the form \[86724\].
Note:In such types of questions the key concept we have to remember is that there is always the divisibility rule of $3$ which is stated above.
After that we can easily find the smallest digit and the largest digit in the blank space for the given question.
Complete step-by-step answer:
It is given that the given number is $\_6724$
We have to find the blank space at smallest and greatest digit and it is divisible by \[3\]
A number is divisible by \[3\] if the sum of its digits is divisible by\[3\].
Now we have to sum of digits in the given number =$\_ + 6 + 7 + 2 + 4 = \_ + 19$
Then we need to check numbers for blank space to give sum would be divisible by 3
![seo images](https://www.vedantu.com/question-sets/b461fe00-a105-41eb-a27b-7ce1651f3f1d1915962604683861185.png)
We can see here on simplifications the digits which when added them in the result $\left( {19} \right)$ gives the final number will divisible by $3$
Hence we got the smallest digit will be $2$ which will be of the form \[26724\] and we got the greatest digit will be $8$ which will be of the form \[86724\].
Note:In such types of questions the key concept we have to remember is that there is always the divisibility rule of $3$ which is stated above.
After that we can easily find the smallest digit and the largest digit in the blank space for the given question.
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