Question 124314
# 1


Let's list all of the factors of 48:




Factors of 48:

1,2,3,4,6,8,12,16,24,48


-1,-2,-3,-4,-6,-8,-12,-16,-24,-48 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to 48

1*48

2*24

3*16

4*12

6*8

(-1)*(-48)

(-2)*(-24)

(-3)*(-16)

(-4)*(-12)

(-6)*(-8)


note: remember two negative numbers multiplied together make a positive number



Now which of these pairs add to 14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 14


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">48</td><td>1+48=49</td></tr><tr><td align="center">2</td><td align="center">24</td><td>2+24=26</td></tr><tr><td align="center">3</td><td align="center">16</td><td>3+16=19</td></tr><tr><td align="center">4</td><td align="center">12</td><td>4+12=16</td></tr><tr><td align="center">6</td><td align="center">8</td><td>6+8=14</td></tr><tr><td align="center">-1</td><td align="center">-48</td><td>-1+(-48)=-49</td></tr><tr><td align="center">-2</td><td align="center">-24</td><td>-2+(-24)=-26</td></tr><tr><td align="center">-3</td><td align="center">-16</td><td>-3+(-16)=-19</td></tr><tr><td align="center">-4</td><td align="center">-12</td><td>-4+(-12)=-16</td></tr><tr><td align="center">-6</td><td align="center">-8</td><td>-6+(-8)=-14</td></tr></table>



From this list we can see that 6 and 8 add up to 14 and multiply to 48




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# 2



Let's list all of the factors of -72:




Factors of -72:

1,2,3,4,6,8,9,12,18,24,36,72


-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-36,-72 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to -72

(1)*(-72)

(2)*(-36)

(3)*(-24)

(4)*(-18)

(6)*(-12)

(8)*(-9)

(-1)*(72)

(-2)*(36)

(-3)*(24)

(-4)*(18)

(-6)*(12)

(-8)*(9)


note: remember, the product of a negative and a positive number is a negative number



Now which of these pairs add to -21? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -21


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">-72</td><td>1+(-72)=-71</td></tr><tr><td align="center">2</td><td align="center">-36</td><td>2+(-36)=-34</td></tr><tr><td align="center">3</td><td align="center">-24</td><td>3+(-24)=-21</td></tr><tr><td align="center">4</td><td align="center">-18</td><td>4+(-18)=-14</td></tr><tr><td align="center">6</td><td align="center">-12</td><td>6+(-12)=-6</td></tr><tr><td align="center">8</td><td align="center">-9</td><td>8+(-9)=-1</td></tr><tr><td align="center">-1</td><td align="center">72</td><td>-1+72=71</td></tr><tr><td align="center">-2</td><td align="center">36</td><td>-2+36=34</td></tr><tr><td align="center">-3</td><td align="center">24</td><td>-3+24=21</td></tr><tr><td align="center">-4</td><td align="center">18</td><td>-4+18=14</td></tr><tr><td align="center">-6</td><td align="center">12</td><td>-6+12=6</td></tr><tr><td align="center">-8</td><td align="center">9</td><td>-8+9=1</td></tr></table>



From this list we can see that 3 and -24 add up to -21 and multiply to -72