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What is the smallest number to be placed in the place of $x$ in the number $317x2$ so that the number formed is divisible by 9?
Given :
The given number $317x2$ is divisible by 9.
To do :
We have to find the smallest number to be placed in the place of x.
Solution :
Divisibility rule of 9:
The rule for divisibility by 9 is similar to the divisibility rule for 3. That is, if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.
Therefore,
Sum of the digits in $317x2 = 3+1+7+x+2 = 13+x$
$13+x$ should be divisible by 9 so that the number formed is divisible by 9.
If $x = 5$,
$13+x = 13+5 = 18$ and 18 is divisible by 9.
Therefore,
The smallest number to be placed in the place of x in the number 317x2 so that the number formed is divisible by 9 is 5.
Updated on: 10-Oct-2022
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