Courses for Kids
Free study material
Offline Centres
Store Icon

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: 21st Jul 2024
Total views: 450.9k
Views today: 7.50k
450.9k+ 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.