How to solve (a) 68436/12

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) 68436/12 | Equatix

Use the $1^{st}$ digit $6$ from dividend $68436$

$$\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)68436}\\\end{array}$$

Since $6$ is less than $12$, use the next digit $8$ from dividend $68436$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)68436}\\\end{array}$$

Use the $2^{nd}$ digit $8$ from dividend $68436$

$$\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)68436}\\\end{array}$$

Find closest multiple of $12$ to $68$. We see that $5 \times 12 = 60$ is the nearest. Now subtract $60$ from $68$ to get reminder $8$. Add $5$ to quotient.

$$\begin{array}{l}\phantom{12)}05\phantom{4}\\12\overline{)68436}\\\phantom{12)}\underline{\phantom{}60\phantom{999}}\\\phantom{12)9}8\\\end{array}$$

Use the $3^{rd}$ digit $4$ from dividend $68436$

$$\begin{array}{l}\phantom{12)}05\phantom{5}\\12\overline{)68436}\\\phantom{12)}\underline{\phantom{}60\phantom{999}}\\\phantom{12)9}84\\\end{array}$$

Find closest multiple of $12$ to $84$. We see that $7 \times 12 = 84$ is the nearest. Now subtract $84$ from $84$ to get reminder $0$. Add $7$ to quotient.

$$\begin{array}{l}\phantom{12)}057\phantom{6}\\12\overline{)68436}\\\phantom{12)}\underline{\phantom{}60\phantom{999}}\\\phantom{12)9}84\\\phantom{12)}\underline{\phantom{9}84\phantom{99}}\\\phantom{12)999}0\\\end{array}$$

Use the $4^{th}$ digit $3$ from dividend $68436$

$$\begin{array}{l}\phantom{12)}057\phantom{7}\\12\overline{)68436}\\\phantom{12)}\underline{\phantom{}60\phantom{999}}\\\phantom{12)9}84\\\phantom{12)}\underline{\phantom{9}84\phantom{99}}\\\phantom{12)999}3\\\end{array}$$

Since $3$ is less than $12$, use the next digit $6$ from dividend $68436$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{12)}0570\phantom{8}\\12\overline{)68436}\\\phantom{12)}\underline{\phantom{}60\phantom{999}}\\\phantom{12)9}84\\\phantom{12)}\underline{\phantom{9}84\phantom{99}}\\\phantom{12)999}3\\\end{array}$$

Use the $5^{th}$ digit $6$ from dividend $68436$

$$\begin{array}{l}\phantom{12)}0570\phantom{9}\\12\overline{)68436}\\\phantom{12)}\underline{\phantom{}60\phantom{999}}\\\phantom{12)9}84\\\phantom{12)}\underline{\phantom{9}84\phantom{99}}\\\phantom{12)999}36\\\end{array}$$

Find closest multiple of $12$ to $36$. We see that $3 \times 12 = 36$ is the nearest. Now subtract $36$ from $36$ to get reminder $0$. Add $3$ to quotient.

$$\begin{array}{l}\phantom{12)}05703\phantom{10}\\12\overline{)68436}\\\phantom{12)}\underline{\phantom{}60\phantom{999}}\\\phantom{12)9}84\\\phantom{12)}\underline{\phantom{9}84\phantom{99}}\\\phantom{12)999}36\\\phantom{12)}\underline{\phantom{999}36\phantom{}}\\\phantom{12)99999}0\\\end{array}$$

Since $0$ is less than $12$, stop the division. The reminder is $0$. The topmost line $05703$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $5703$.

$$\text{Quotient: }5703$$ $$\text{Reminder: }0$$

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