Replace * in the number 835*86 by the smallest number to make it divisible by 9.
Answers
if *=6
30+6=36 is divisible by 9
The smallest number with which * can be replaced to make the number 835*86 divisible by 9, is 6.
Given,
The number:
835*86.
To find,
The smallest number with which * can be replaced to make the given number divisible by 9.
Solution,
It can be seen that the number given here is
835*86.
We need to replace the * with the smallest number so as to make the above number divisible by 9.
Now, from the divisibility rule of 9, we know that,
- a number is divisible by 9 when the sum of all of the digits of this number is divisible by 9.
Here, for the given number, we can see that the sum of digits is
= 8 + 3 + 5 + * + 8 + 6
= 30 + *
⇒ 30 + * needs to be a multiple of 9.
It can be observed that the number after 30 which is divisible by 9, is 36.
So, we can say,
30 + * = 36
⇒ * = 36 - 30
⇒ * = 6.
Therefore, the smallest number with which * can be replaced to make the number 835*86 divisible by 9, is 6.
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