Question

Is the number of factor pairs for a number equal to the number of arrays for the same number explain

Answer 1

Yes they are the same because they equal each other

Answer 2

Answer: False if we are using reals or integers, true if we are using natural numbers.

Step-by-step explanation: Suppose you want to craft the number 20.

The arrays are; 1x20, 2x10, 4x5

So you have 3 arrays (and other 3 for the conmutative property)

And the factor pairs in principle would be the same:

1*20 = 20

2*10 = 20

4*5 = 20

So we have:

1, 2, 4, 5, 10, 20

But, as you may know, when we multiply a negative number by other negative number, the result is a positive number.

So (-1)*(-20) = 20 is also a factor pair.

Then, if we accept negtive numbers, this means that there are twice as many factor pairs as arrays (Because there are not negative arrays)

In case we are only using natural numbers (there are no negative numbers) then the number of pair factors is equal as the number of arrays, is easy to see this because for each pair factor, you can take the first number and with it make the number of rows, and then take the second number and make the number of columns, and then for each factor pair you also have one array.