Finding Minimum Value for Divisibility by 9

The question asks for the minimum digit 'x' that makes the number 2346x45 divisible by 9.

Divisibility Rule for 9

A number is exactly divisible by 9 if the sum of its digits is divisible by 9.

Applying the Rule

Let the number be $N = 2346x45$.

The sum of the digits of N is:

Calculate the sum of the known digits:

For N to be divisible by 9, the sum S must be a multiple of 9.

Determining the Minimum Value of 'x'

We need to find the smallest single digit (0-9) for 'x' such that $24 + x$ is a multiple of 9.

• List multiples of 9: 9, 18, 27, 36, ...
• Test values for $24 + x$:
  • If $24 + x = 27$, then $x = 27 - 24 = 3$.

Since $x=3$ is a single digit and is the smallest value that satisfies the condition, it is the minimum value required.

Therefore, the minimum value for 'x' is 3.