Question

Which counterexample shows that the following conjecture is false? Every perfect square number has exactly three factors. * F The factors of 2 are 1, 2. G The factors of 4 are 1, 2, 4. H The factors of 8 are 1, 2, 4, 8. I The factors of 16 are 1, 2, 4, 8, 16.

Answer 1

option I is a counter example of the conjecture.

Step-by-step explanation:

The conjecture: Every perfect square number has exactly three factors.

For the options given to be a counter example, it must satisfy a perfect square but the factors cannot be exactly 3.

Perfect square: multiplication of same numbers

F: 2 is not a perfect square. This statement cannot be used

H: 8 is also not a perfect square. This won't apply

G: 4 is a perfect square. But the factors of 4 are three in muber.

So, we can't consider it.

I: 16 is a perfect square. Its factors are more than 3.

Hence, option I is a counter example of the conjecture.