How to solve (35706)/(13)

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 (35706)/(13) | Equatix

Question

$$\frac{ 35706 }{ 13 }$$

Evaluate

$\frac{35706}{13}\approx 2746.615384615$

Steps For Long Division Method

Use the $1^{st}$ digit $3$ from dividend $35706$

$$\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)35706}\\\end{array}$$

Since $3$ is less than $13$, use the next digit $5$ from dividend $35706$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)35706}\\\end{array}$$

Use the $2^{nd}$ digit $5$ from dividend $35706$

$$\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)35706}\\\end{array}$$

Find closest multiple of $13$ to $35$. We see that $2 \times 13 = 26$ is the nearest. Now subtract $26$ from $35$ to get reminder $9$. Add $2$ to quotient.

$$\begin{array}{l}\phantom{13)}02\phantom{4}\\13\overline{)35706}\\\phantom{13)}\underline{\phantom{}26\phantom{999}}\\\phantom{13)9}9\\\end{array}$$

Use the $3^{rd}$ digit $7$ from dividend $35706$

$$\begin{array}{l}\phantom{13)}02\phantom{5}\\13\overline{)35706}\\\phantom{13)}\underline{\phantom{}26\phantom{999}}\\\phantom{13)9}97\\\end{array}$$

Find closest multiple of $13$ to $97$. We see that $7 \times 13 = 91$ is the nearest. Now subtract $91$ from $97$ to get reminder $6$. Add $7$ to quotient.

$$\begin{array}{l}\phantom{13)}027\phantom{6}\\13\overline{)35706}\\\phantom{13)}\underline{\phantom{}26\phantom{999}}\\\phantom{13)9}97\\\phantom{13)}\underline{\phantom{9}91\phantom{99}}\\\phantom{13)99}6\\\end{array}$$

Use the $4^{th}$ digit $0$ from dividend $35706$

$$\begin{array}{l}\phantom{13)}027\phantom{7}\\13\overline{)35706}\\\phantom{13)}\underline{\phantom{}26\phantom{999}}\\\phantom{13)9}97\\\phantom{13)}\underline{\phantom{9}91\phantom{99}}\\\phantom{13)99}60\\\end{array}$$

Find closest multiple of $13$ to $60$. We see that $4 \times 13 = 52$ is the nearest. Now subtract $52$ from $60$ to get reminder $8$. Add $4$ to quotient.

$$\begin{array}{l}\phantom{13)}0274\phantom{8}\\13\overline{)35706}\\\phantom{13)}\underline{\phantom{}26\phantom{999}}\\\phantom{13)9}97\\\phantom{13)}\underline{\phantom{9}91\phantom{99}}\\\phantom{13)99}60\\\phantom{13)}\underline{\phantom{99}52\phantom{9}}\\\phantom{13)999}8\\\end{array}$$

Use the $5^{th}$ digit $6$ from dividend $35706$

$$\begin{array}{l}\phantom{13)}0274\phantom{9}\\13\overline{)35706}\\\phantom{13)}\underline{\phantom{}26\phantom{999}}\\\phantom{13)9}97\\\phantom{13)}\underline{\phantom{9}91\phantom{99}}\\\phantom{13)99}60\\\phantom{13)}\underline{\phantom{99}52\phantom{9}}\\\phantom{13)999}86\\\end{array}$$

Find closest multiple of $13$ to $86$. We see that $6 \times 13 = 78$ is the nearest. Now subtract $78$ from $86$ to get reminder $8$. Add $6$ to quotient.

$$\begin{array}{l}\phantom{13)}02746\phantom{10}\\13\overline{)35706}\\\phantom{13)}\underline{\phantom{}26\phantom{999}}\\\phantom{13)9}97\\\phantom{13)}\underline{\phantom{9}91\phantom{99}}\\\phantom{13)99}60\\\phantom{13)}\underline{\phantom{99}52\phantom{9}}\\\phantom{13)999}86\\\phantom{13)}\underline{\phantom{999}78\phantom{}}\\\phantom{13)9999}8\\\end{array}$$

Since $8$ is less than $13$, stop the division. The reminder is $8$. The topmost line $02746$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $2746$.

$$\text{Quotient: }2746$$ $$\text{Reminder: }8$$

Show Solution

Factor

$\frac{2 \cdot 3 \cdot 11 \cdot 541}{13} = 2746\frac{8}{13} = 2746.6153846153848$

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Steps For Long Division Method

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