Write the smallest digit and the greatest digit in the blank space of the following number so that the number formed is divisible by 3.
${\text{4765}}....{\text{2}}{\text{.}}$
Last updated date: 17th Mar 2023
•
Total views: 308.1k
•
Views today: 2.88k
Answer
308.1k+ views
Hint: -Any number is divisible by 3, if the sum of its digits is divisible by 3.
Given number:
${\text{4765}}....{\text{2}}{\text{.}}$
It is given that the number is divisible by 3.
By the divisibility rule of 3, any number is divisible by 3, if the sum of its digits is divisible by 3.
Let the digit on the blank space be $b$.
\[
4 + 7 + 6 + 5 + b + 2 \\
\Rightarrow b + 24 \\
\]
As we see that 24 is divisible by \[{\text{3 = }}\dfrac{{24}}{3} = 8{\text{ times}}{\text{.}}\]
Therefore in order to make the required number divisible by 3, the least value of $b = 0$ and the maximum value of $b = 9$.
If \[b = 0\], then\[0 + 24 = 24\]. This is divisible by 3.
So, the number becomes 476502
If \[b = 9\], then\[9 + 24 = 33\]. This is divisible by 3.
So, the number becomes 476592
Therefore the smallest digit is 0 and the greatest digit is 9.
Note: - In such types of questions the key concept we have to remember is that always remember the divisibility rule of 3 which is stated above, then according to this rule calculate the minimum and maximum value in the black space so that number is exactly divisible by 3.
Given number:
${\text{4765}}....{\text{2}}{\text{.}}$
It is given that the number is divisible by 3.
By the divisibility rule of 3, any number is divisible by 3, if the sum of its digits is divisible by 3.
Let the digit on the blank space be $b$.
\[
4 + 7 + 6 + 5 + b + 2 \\
\Rightarrow b + 24 \\
\]
As we see that 24 is divisible by \[{\text{3 = }}\dfrac{{24}}{3} = 8{\text{ times}}{\text{.}}\]
Therefore in order to make the required number divisible by 3, the least value of $b = 0$ and the maximum value of $b = 9$.
If \[b = 0\], then\[0 + 24 = 24\]. This is divisible by 3.
So, the number becomes 476502
If \[b = 9\], then\[9 + 24 = 33\]. This is divisible by 3.
So, the number becomes 476592
Therefore the smallest digit is 0 and the greatest digit is 9.
Note: - In such types of questions the key concept we have to remember is that always remember the divisibility rule of 3 which is stated above, then according to this rule calculate the minimum and maximum value in the black space so that number is exactly divisible by 3.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

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

A Short Paragraph on our Country India
