We need to factor the expression $4+10.$

Let's find the greatest common factor of $4$ and $10.$ We list the factors of each number. Then, we find the largest number that appears in both lists:

• Factors of $4{:}$ $\quad 1, {\color{blue}2}, 4$

• Factors of $10{:}$ $\quad 1, {\color{blue}2}, 5, 10$

So the greatest common factor of $4$ and $10$ is ${\color{blue}{2}}.$

Next, we write each number as a product of the greatest common factor and another factor:

• $4 = {\color{blue}2} \times {\color{red}{2}}$

• $10 = {\color{blue}2} \times {\color{red}{5}}$

Finally, to factor the given expression, we place the greatest common factor ${\color{blue}2}$ outside the parentheses and leave the sum of the other two factors inside the parentheses: \[ 4+10=\underbrace{{\color{blue}{2}}\times {\color{red}2}}_{4} + \underbrace{{\color{blue}{2}}\times {\color{red}5}}_{10} = {\color{blue}{2}}({\color{red}2} + {\color{red}5}) \]

So the missing number is $2.$

We need to factor the expression $3+15.$

Let's find the greatest common factor of $3$ and $15.$ We list the factors of each number. Then, we find the largest number that appears in both lists:

• Factors of $3{:}$ $\quad 1, {\color{blue}3}$

• Factors of $15{:}$ $\quad 1, {\color{blue}3}, 5, 15$

So the greatest common factor of $3$ and $15$ is ${\color{blue}{3}}.$

Next, we write each number as a product of the greatest common factor and another factor:

• $3 = {\color{blue}3} \times {\color{red}{1}}$

• $15 = {\color{blue}3} \times {\color{red}{5}}$

Finally, to factor the given expression, we place the greatest common factor ${\color{blue}3}$ outside the parentheses and leave the sum of the other two factors inside the parentheses: \[ 3+15=\underbrace{{\color{blue}{3}} \times {\color{red}1}}_{3} + \underbrace{{\color{blue}{3}}\times {\color{red}5}}_{15} = {\color{blue}{3}}({\color{red}1}+{\color{red}5}) \]

So the missing number is $3.$

We need to factor the expression $16+40.$

Let's find the greatest common factor of $16$ and $40.$ We list the factors of each number. Then, we find the largest number that appears in both lists:

• Factors of $16{:}$ $\quad 1, 2, 4, {\color{blue}8}, 16$

• Factors of $40{:}$ $\quad 1, 2, 4, 5, {\color{blue}8}, 10, 20, 40$

So the greatest common factor of $16$ and $40$ is ${\color{blue}{8}}.$

Next, we write each number as a product of the greatest common factor and another factor:

• $16 = {\color{blue}8} \times {\color{red}{2}}$

• $40 = {\color{blue}8} \times {\color{red}{5}}$

Finally, to factor the given expression, we place the greatest common factor ${\color{blue}8}$ outside the parentheses and leave the sum of the other two factors inside the parentheses: \[ 16+40=\underbrace{{\color{blue}{8}}\times {\color{red}2}}_{16} + \underbrace{{\color{blue}{8}}\times {\color{red}5}}_{40} = {\color{blue}{8}}({\color{red}2} + {\color{red}5}) \]

So the missing number is $8.$

Let's find the greatest common factor of $6$ and $4.$ We list the factors of each number. Then, we find the largest number that appears in both lists:

• Factors of $6$: $\quad 1, {\color{blue}2}, 3, 6$

• Factors of $4$: $\quad 1, {\color{blue}2}, 4$

So the greatest common factor of $6$ and $4$ is ${\color{blue}{2}}.$

Next, we write each number as a product of the greatest common factor and another factor:

• $6 = {\color{blue}2} \times {\color{red}{3}}$

• $4 = {\color{blue}2} \times {\color{red}{2}}$

Finally, to factor the given expression, we place the greatest common factor ${\color{blue}2}$ outside the parentheses and leave the sum of the other two factors inside the parentheses: \[ 6+4=\underbrace{{\color{blue}{2}}\times {\color{red}3}}_{6} + \underbrace{{\color{blue}{2}}\times {\color{red}2}}_{4} = {\color{blue}{2}}({\color{red}3} + {\color{red}2}) \]

Therefore, the expression $6+4$ factors into $2(3+2).$

Let's find the greatest common factor of $9$ and $6.$ We list the factors of each number. Then, we find the largest number that appears in both lists:

• Factors of $9$: $\quad 1, {\color{blue}3}, 9$

• Factors of $6$: $\quad 1, 2, {\color{blue}3}, 6$

So the greatest common factor of $9$ and $6$ is ${\color{blue}{3}}.$

Next, we write each number as a product of the greatest common factor and another factor:

• $9 = {\color{blue}3} \times {\color{red}{3}}$

• $6 = {\color{blue}3} \times {\color{red}{2}}$

Finally, to factor the given expression, we place the greatest common factor ${\color{blue}3}$ outside the parentheses and leave the sum of the other two factors inside the parentheses: \[ 9+6=\underbrace{{\color{blue}{3}}\times {\color{red}3}}_{9} + \underbrace{{\color{blue}{3}}\times {\color{red}2}}_{6} = {\color{blue}{3}}({\color{red}3} + {\color{red}2}) \]

Therefore, the expression $9 + 6$ factors into $3(3 + 2).$

Let's find the greatest common factor of $25$ and $80.$ We list the factors of each number. Then, we find the largest number that appears in both lists:

• Factors of $25$: $\quad 1, {\color{blue}5}, 25$

• Factors of $80$: $\quad 1, 2, 4, {\color{blue}5}, 8, 10, 16, 20, 40, 80$

So the greatest common factor of $25$ and $80$ is ${\color{blue}{5}}.$

Next, we write each number as a product of the greatest common factor and another factor:

• $25 = {\color{blue}5} \times {\color{red}{5}}$

• $80 = {\color{blue}5} \times {\color{red}{16}}$

Finally, to factor the given expression, we place the greatest common factor $\color{blue}5$ outside the parentheses and leave the sum of the other two factors inside the parentheses: \[ 25+80=\underbrace{{\color{blue}{5}} \times {\color{red}5}}_{25} + \underbrace{{\color{blue}{5}} \times {\color{red}16}}_{80} = {\color{blue}{5}}({\color{red}5} + {\color{red}16}) \]

Therefore, the expression $25 + 80$ factors into $5(5 + 16).$

Let's find the greatest common factor of $12$ and $16.$ We list the factors of each number. Then, we find the largest number that appears in both lists:

• Factors of $12$: $\quad 1, 2, 3, {\color{blue}4}, 6, 12$

• Factors of $16$: $\quad 1, 2, {\color{blue}4}, 8, 16$

So the greatest common factor of $12$ and $16$ is ${\color{blue}{4}}.$

Next, we write each number as a product of the greatest common factor and another factor:

• $12 = {\color{blue}4} \times {\color{red}{3}}$

• $16 = {\color{blue}4} \times {\color{red}{4}}$

Finally, to factor the given expression, we place the greatest common factor ${\color{blue}4}$ outside the parentheses and leave the sum of the other two factors inside the parentheses: \[ 12+16=\underbrace{{\color{blue}{4}}\times {\color{red}3}}_{12} + \underbrace{{\color{blue}{4}}\times {\color{red}4}}_{16} = {\color{blue}{4}}({\color{red}3} + {\color{red}4}) \]

Therefore, the expression $12+16$ factors into $4(3+4).$

Let's find the greatest common factor of $14$ and $35.$ We list the factors of each number. Then, we find the largest number that appears in both lists:

• Factors of $14$: $\quad 1, 2, {\color{blue}7}, 14$

• Factors of $35$: $\quad 1, 5, {\color{blue}7}, 35$

So the greatest common factor of $14$ and $35$ is ${\color{blue}{7}}.$

Next, we write each number as a product of the greatest common factor and another factor:

• $14 = {\color{blue}7} \times {\color{red}{2}}$

• $35 = {\color{blue}7} \times {\color{red}{5}}$

Finally, to factor the given expression, we place the greatest common factor ${\color{blue}7}$ outside the parentheses and leave the sum of the other two factors inside the parentheses: \[ 14+35=\underbrace{{\color{blue}{7}}\times {\color{red}2}}_{14} + \underbrace{{\color{blue}{7}}\times {\color{red}5}}_{35} = {\color{blue}{7}}({\color{red}2} + {\color{red}5}) \]

Therefore, the expression $14 + 35$ factors into $7(2 + 5).$