Question

The smallest number $x$ such that $4456 + x$ is divisible by 7 is

• A. 3
• B. 4
• C. 2
• D. 5

Hint:

Smallest addition = Divisor − Remainder.

Answer 1

The Correct Option is A

To find the smallest number \(x\) such that \(4456 + x\) is divisible by \(7\), we follow the steps below:

1. First, determine the remainder when \(4456\) is divided by \(7\). This can be done through direct division.

Divide \(4456\) by \(7\).

Calculation

4456 ÷ 7 = 636

Remainder: 4

1. Since the remainder is \(4\), the expression \(4456\) can be expressed as:

\(4456 = 7 \times 636 + 4\)

1. We want \(4456 + x\) to be divisible by \(7\). Therefore,

\(4456 + x \equiv 0 \pmod{7}\)

Substituting the remainder, this becomes:

\(4 + x \equiv 0 \pmod{7}\)

1. To find \(x\), solve the equation:

\(x \equiv -4 \equiv 3 \pmod{7}\)

The smallest non-negative integer solution for \(x\) is \(3\).

Hence, the smallest number \(x\) such that \(4456 + x\) is divisible by \(7\) is 3.