# Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3. Find _6724.

Last updated date: 19th Mar 2023

•

Total views: 305.7k

•

Views today: 7.84k

Answer

Verified

305.7k+ views

Hint: Find the sum of digits of the given number. Apply natural numbers from 0-9 in the blank space. A number is divisible by 3, if the sum of the digits are divisible by 3. Substitute different values in the sum and check divisibility.

Complete step-by-step answer:

We know that a number is divisible by 3, if the sum of the digits are divisible by 3.

We have to find the missing number in _6724.

The sum of the digits _6724 = _+6+7+2+4 = _+19.

Now we have to check different values for the blank digit and check if the number is divisible by 3.

Sum of digit = _+19

Let us put 0 to 9 digits in the blank space.

Let’s put variable ‘x’ in the blank space for easy calculation.

$\therefore $Sum of digit= x+19

Let’s put x=0, sum = 19+0=19

x=1, sum=19+1=20

x=2, sum=19+1=21

x=3, sum=19+1=22

x=4, sum=19+1=23

x=5, sum=19+1=24

x=6, sum=19+1=25

x=7, sum=19+1=26

x=8, sum=19+1=27

x=9, sum=19+1=28

From the above possibilities,

x=2, sum=21, is divisible by 3.

x=5, sum=24, is divisible by 3.

x=8, sum=27, is divisible by 3.

$\therefore $The smallest digit in blank space = 2.

The greatest digit in blank space =8.

Therefore the no. formed are 26724 and 86724

Note: Here we used to find a single digit to fit the blank space, that’s why the natural nos from 0-9 were considered.

Complete step-by-step answer:

We know that a number is divisible by 3, if the sum of the digits are divisible by 3.

We have to find the missing number in _6724.

The sum of the digits _6724 = _+6+7+2+4 = _+19.

Now we have to check different values for the blank digit and check if the number is divisible by 3.

Sum of digit = _+19

Let us put 0 to 9 digits in the blank space.

Let’s put variable ‘x’ in the blank space for easy calculation.

$\therefore $Sum of digit= x+19

Let’s put x=0, sum = 19+0=19

x=1, sum=19+1=20

x=2, sum=19+1=21

x=3, sum=19+1=22

x=4, sum=19+1=23

x=5, sum=19+1=24

x=6, sum=19+1=25

x=7, sum=19+1=26

x=8, sum=19+1=27

x=9, sum=19+1=28

From the above possibilities,

x=2, sum=21, is divisible by 3.

x=5, sum=24, is divisible by 3.

x=8, sum=27, is divisible by 3.

$\therefore $The smallest digit in blank space = 2.

The greatest digit in blank space =8.

Therefore the no. formed are 26724 and 86724

Note: Here we used to find a single digit to fit the blank space, that’s why the natural nos from 0-9 were considered.

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

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

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

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

Name the Largest and the Smallest Cell in the Human Body ?