Question

Find the possible pairs of integers that give a product of -100

Answer 1

Answer:

The all possible pairs are:

(i) -100&1

(ii) -50&2

(iii) -25&4

(iv) -20&5

(v) -10&10

Answer 2

Answer:

The possible pairs of integers are $(1,-100)$, $(-1,100)$, $(2,-50)$, $(-2,50)$, $(20,-5)$, $(-20,5)$, $(-25,4)$, $(25,-4)$, $(-10,10)$ and $(10,-10)$.

Step-by-step explanation:

To find the possible pairs of integers that give a product of $-100$.

Consider the prime factorisation of the number $100$ as follows:

$100=1\times2\times2\times5\times5$

The possible pairs of integers are:

1) 1 and $-100$

Product of 1 and $-100$ is,

$1\times (-100)=-100$

Thus, $(1,-100)$ is a pair of integers.

2) -1 and $100$

Product of -1 and 100 is,

$-1\times 100=-100$

Thus, $(-1,100)$ is a pair of integers.

3) 2 and -50

Product of 2 and -50 is,

$2\times (-50)=-100$

Thus, $(2,-50)$ is a pair of integers.

4) -2 and 50

Product of -2 and 50 is,

$-2\times 50=-100$

Thus, $(-2,50)$ is a pair of integers.

5) 20 and -5

Product of 20 and -5 is,

$20\times (-5)=-100$

Thus, $(20,-5)$ is a pair of integers.

6) -20 and 5

Product of -20 and 5 is,

$-20\times 5=-100$

Thus, $(-20,5)$ is a pair of integers.

7) -25 and 4

Product of -25 and 4 is,

$-25\times 4=-100$

Thus, $(-25,4)$ is a pair of integers.

8) 25 and -4

Product of 25 and -4 is,

$25\times (-4)=-100$

Thus, $(25,-4)$ is a pair of integers.

9) 10 and -10

Product of 10 and -10 is,

$10\times (-10)=-100$

Thus, $(10,-10)$ is a pair of integers.

10) -10 and 10

Product of -10 and 10 is,

$-10\times 10=-100$

Thus, $(-10,10)$ is a pair of integers.

Therefore, $(1,-100)$, $(-1,100)$, $(2,-50)$, $(-2,50)$, $(20,-5)$, $(-20,5)$, $(-25,4)$, $(25,-4)$, $(-10,10)$ and $(10,-10)$ are the 10 possible pairs of integers that give a product of -100.

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