Finding Least Value for Divisibility by 9

The question asks for the smallest digit '$x$' that makes the number '$7x5462$' divisible by 9.

Divisibility Rule for 9

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

Applying the Rule

First, find the sum of the known digits in the number '$7x5462$':

Sum = $7 + 5 + 4 + 6 + 2 = 24$.

The total sum of the digits is $24 + x$.

For the number to be divisible by 9, the sum '$24 + x$' must be a multiple of 9.

Determining the Least Value of x

We need to find the smallest possible digit (0-9) for '$x$' such that '$24 + x$' is a multiple of 9. Let's test the values:

• If $x=0$, Sum $= 24 + 0 = 24$. Not divisible by 9.
• If $x=1$, Sum $= 24 + 1 = 25$. Not divisible by 9.
• If $x=2$, Sum $= 24 + 2 = 26$. Not divisible by 9.
• If $x=3$, Sum $= 24 + 3 = 27$. Since $27 = 9 \times 3$, this is divisible by 9.

The least value for '$x$' that satisfies the condition is 3.