Why the statement is false (beginner-friendly):
Exactly divides means: a number d divides n if there is no remainder. We write this as \(d \mid n\).
Counterexample (step by step):
- Choose the divisor \(d = 3\).
- Choose three numbers: \(1\), \(2\), and \(3\).
- Add them: \(1 + 2 + 3 = 6\).
- Check if 3 divides the sum: \(3 \mid 6\) because \(\dfrac{6}{3} = 2\) (no remainder).
- Now check each number separately:
• \(\dfrac{1}{3}\) leaves a remainder → \(3 \nmid 1\).
• \(\dfrac{2}{3}\) leaves a remainder → \(3 \nmid 2\).
• \(\dfrac{3}{3} = 1\) → \(3 \mid 3\). - 3 does not divide all three numbers separately (it fails for 1 and 2).
Therefore, the statement is false.