Question

which counterexample shows that the following conjecture is false?
F. the factors of 2 are1,2.
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

yes

Answer 2

what is the conjecture?

Answer 3

I.

Answer 4

The conjecture is:

Every perfect square number has exactly three factors

Answer 5

i apologize for not including it

Answer 6

Since they want a counterexample to the conjecture, Every perfect square number has exactly three factors:

Pick the answer choice that is a perfect squares but has more or less than three factors.

Answer 7

i think it is I

Answer 8

The first choice is considering factors of 2. Since 2 is not a perfect square we can eliminate this choice. Similarly, the third choice is considering factors of 8 which is not a perfect square and so that can be eliminated too.

Choice 2 considers factors of 4. 4 is a perfect square. And is has 3 factors. This supports the original conjecture but we want a counterexample. So this can be eliminated.

So we are left with the last choice.

Answer 9

16 is a perfect square and it has five factors. This is a counterexample to the original conjecture.