Question

If the product of six integers is negative, at most how many of the integers can be negative?

Answer 1

It have to be odd number. So, it is 5. Minus multiplied on minus gives plus. You have to multiply odd number of negative integers to positive integers to get negative product.

Answer 2

In order for the product of six integers to be negative, there must be an odd number of negative integers among them. This is because the product of an odd number of negative numbers is negative, and the product of an even number of negative numbers is positive.

So, at most, five of the integers can be negative, and one must be positive to have a total of six integers with an odd number of negatives.

Answer 3

To have a negative product, there must be an odd number of negative factors. If there are zero negative factors, the product will be positive. If there are two negative factors, the product will still be positive. However, if there are four negative factors, the product will be negative. Similarly, if there are six negative factors, the product will also be negative. So the maximum number of integers that can be negative is $\boxed{6}$.

Answer 4

To have the product of six integers be negative, you need an odd number of negative integers. This is because when you multiply an even number of negative integers, the result is positive, and when you multiply an odd number of negative integers, the result is negative.

So, the most you can have is five integers being negative. If you have six negative integers, the product would be positive.

Answer 5

Since you have six integers in total, you can have at most five of them be negative (an odd number), and the remaining one should be positive. This will ensure that you have an odd number of negative integers, resulting in a negative product.

Answer 6

If the product of 6 integers are negative then 

one, three or five at most can be negative.

Prove

Lets use the first 6 natural numbers as our integer.

That is 1,2,3,4,5,6

Then

-1×2×3×4×5×6=-720.                     For one (-) number 

1×(-2)×(-3)×(-4)×5×6=-720.          For three (-) numbers

-1×(-2)×(-3)×(-4)×(-5)×6=-720      For five (-) numbers 

This completes the prove that at most 5 of those integers must be negative for the the product of the integers to be negative.

Answer 7

If the product of six integers is negative, then it shows that an odd number of them is negative. In these case, five of the integers is surely negative.