How to solve ( a ) 7038421/639

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve ( a ) 7038421/639 | Equatix

Use the $1^{st}$ digit $7$ from dividend $7038421$

$$\begin{array}{l}\phantom{639)}\phantom{1}\\639\overline{)7038421}\\\end{array}$$

Since $7$ is less than $639$, use the next digit $0$ from dividend $7038421$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{639)}0\phantom{2}\\639\overline{)7038421}\\\end{array}$$

Use the $2^{nd}$ digit $0$ from dividend $7038421$

$$\begin{array}{l}\phantom{639)}0\phantom{3}\\639\overline{)7038421}\\\end{array}$$

Since $70$ is less than $639$, use the next digit $3$ from dividend $7038421$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{639)}00\phantom{4}\\639\overline{)7038421}\\\end{array}$$

Use the $3^{rd}$ digit $3$ from dividend $7038421$

$$\begin{array}{l}\phantom{639)}00\phantom{5}\\639\overline{)7038421}\\\end{array}$$

Find closest multiple of $639$ to $703$. We see that $1 \times 639 = 639$ is the nearest. Now subtract $639$ from $703$ to get reminder $64$. Add $1$ to quotient.

$$\begin{array}{l}\phantom{639)}001\phantom{6}\\639\overline{)7038421}\\\phantom{639)}\underline{\phantom{}639\phantom{9999}}\\\phantom{639)9}64\\\end{array}$$

Use the $4^{th}$ digit $8$ from dividend $7038421$

$$\begin{array}{l}\phantom{639)}001\phantom{7}\\639\overline{)7038421}\\\phantom{639)}\underline{\phantom{}639\phantom{9999}}\\\phantom{639)9}648\\\end{array}$$

Find closest multiple of $639$ to $648$. We see that $1 \times 639 = 639$ is the nearest. Now subtract $639$ from $648$ to get reminder $9$. Add $1$ to quotient.

$$\begin{array}{l}\phantom{639)}0011\phantom{8}\\639\overline{)7038421}\\\phantom{639)}\underline{\phantom{}639\phantom{9999}}\\\phantom{639)9}648\\\phantom{639)}\underline{\phantom{9}639\phantom{999}}\\\phantom{639)999}9\\\end{array}$$

Use the $5^{th}$ digit $4$ from dividend $7038421$

$$\begin{array}{l}\phantom{639)}0011\phantom{9}\\639\overline{)7038421}\\\phantom{639)}\underline{\phantom{}639\phantom{9999}}\\\phantom{639)9}648\\\phantom{639)}\underline{\phantom{9}639\phantom{999}}\\\phantom{639)999}94\\\end{array}$$

Since $94$ is less than $639$, use the next digit $2$ from dividend $7038421$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{639)}00110\phantom{10}\\639\overline{)7038421}\\\phantom{639)}\underline{\phantom{}639\phantom{9999}}\\\phantom{639)9}648\\\phantom{639)}\underline{\phantom{9}639\phantom{999}}\\\phantom{639)999}94\\\end{array}$$

Use the $6^{th}$ digit $2$ from dividend $7038421$

$$\begin{array}{l}\phantom{639)}00110\phantom{11}\\639\overline{)7038421}\\\phantom{639)}\underline{\phantom{}639\phantom{9999}}\\\phantom{639)9}648\\\phantom{639)}\underline{\phantom{9}639\phantom{999}}\\\phantom{639)999}942\\\end{array}$$

Find closest multiple of $639$ to $942$. We see that $1 \times 639 = 639$ is the nearest. Now subtract $639$ from $942$ to get reminder $303$. Add $1$ to quotient.

$$\begin{array}{l}\phantom{639)}001101\phantom{12}\\639\overline{)7038421}\\\phantom{639)}\underline{\phantom{}639\phantom{9999}}\\\phantom{639)9}648\\\phantom{639)}\underline{\phantom{9}639\phantom{999}}\\\phantom{639)999}942\\\phantom{639)}\underline{\phantom{999}639\phantom{9}}\\\phantom{639)999}303\\\end{array}$$

Use the $7^{th}$ digit $1$ from dividend $7038421$

$$\begin{array}{l}\phantom{639)}001101\phantom{13}\\639\overline{)7038421}\\\phantom{639)}\underline{\phantom{}639\phantom{9999}}\\\phantom{639)9}648\\\phantom{639)}\underline{\phantom{9}639\phantom{999}}\\\phantom{639)999}942\\\phantom{639)}\underline{\phantom{999}639\phantom{9}}\\\phantom{639)999}3031\\\end{array}$$

Find closest multiple of $639$ to $3031$. We see that $4 \times 639 = 2556$ is the nearest. Now subtract $2556$ from $3031$ to get reminder $475$. Add $4$ to quotient.

$$\begin{array}{l}\phantom{639)}0011014\phantom{14}\\639\overline{)7038421}\\\phantom{639)}\underline{\phantom{}639\phantom{9999}}\\\phantom{639)9}648\\\phantom{639)}\underline{\phantom{9}639\phantom{999}}\\\phantom{639)999}942\\\phantom{639)}\underline{\phantom{999}639\phantom{9}}\\\phantom{639)999}3031\\\phantom{639)}\underline{\phantom{999}2556\phantom{}}\\\phantom{639)9999}475\\\end{array}$$

Since $475$ is less than $639$, stop the division. The reminder is $475$. The topmost line $0011014$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $11014$.

$$\text{Quotient: }11014$$ $$\text{Reminder: }475$$

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