To find a counterexample to the conjecture "If a number is divisible by 3, it must also be divisible by 9," we need to find a number that is divisible by 3 but not by 9.
Let's examine each option:
1. **18**: Divisible by 3 (18 ÷ 3 = 6) and also divisible by 9 (18 ÷ 9 = 2).
2. **21**: Divisible by 3 (21 ÷ 3 = 7) but not divisible by 9 (21 ÷ 9 is not an integer).
3. **27**: Divisible by 3 (27 ÷ 3 = 9) and also divisible by 9 (27 ÷ 9 = 3).
4. **54**: Divisible by 3 (54 ÷ 3 = 18) and also divisible by 9 (54 ÷ 9 = 6).
The counterexample to the conjecture is **21**, as it is divisible by 3 but not by 9.
2.
Which is the counterexample to the following conjecture?
If a number is divisible by 3, it must also be divisible by 9.
18
21
27
54
1 answer