a three- digit number 42a divisible by 9 (where a is a single digit number form 1 to 9) find the the value of a
Answers
If the three digit number 24x is divisible by 9 what is the value of x?
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To be able to understand the solution for this question, we need to know about the divisibility of the number 9.
DIVISIBILITY OF THE NUMBER 9:
It states that “a number divisible by 9 should have the sum of its digits equal to a multiple of 9”.
For example: Sum of the digits of the number 585 is 5+8+5=18 and 18 is a multiple of 9. Therefore, 585 will be divisible by 9. We can check this statement to be true because 9×65=585 .
Now, here in this question we know that 24x is divisible by 9. So, the relation between the digits and multiple of 9 will be:
Let m be a factor of the multiple of 9.
2+4+x=9m
6+x=9m
6+x9=m
This is here an equation in two variables. So it should have infinite solutions. But since x is a digit, x could neither be negative nor could be more than 9. And m could only be a natural whole number because the sum of digits of a number could never be negative and in this case it couldn't even be zero because if any of the numbers in an equation of addition is a natural number then the sum should also be a natural number.
Therefore, we should have the values of x between the range 1–9.
We should find it by trial and error method. I can't try them all here, so I am giving you the answer to it now.
The only possible value for x which would satisfy the situations is 3.
Therefore, x=3 .
Answer
3
Step-by-step explanation:
A= 3
The divisibility rule of 9
Total of digits should be divisible by 9
I hope my answer helps you .
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