How to solve (876543)/(234)

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 (876543)/(234) | Equatix

Question

$$\frac{ 876543 }{ 234 }$$

Evaluate

$\frac{292181}{78}\approx 3745.91025641$

Steps For Long Division Method

Use the $1^{st}$ digit $8$ from dividend $876543$

$$\begin{array}{l}\phantom{234)}\phantom{1}\\234\overline{)876543}\\\end{array}$$

Since $8$ is less than $234$, use the next digit $7$ from dividend $876543$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{234)}0\phantom{2}\\234\overline{)876543}\\\end{array}$$

Use the $2^{nd}$ digit $7$ from dividend $876543$

$$\begin{array}{l}\phantom{234)}0\phantom{3}\\234\overline{)876543}\\\end{array}$$

Since $87$ is less than $234$, use the next digit $6$ from dividend $876543$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{234)}00\phantom{4}\\234\overline{)876543}\\\end{array}$$

Use the $3^{rd}$ digit $6$ from dividend $876543$

$$\begin{array}{l}\phantom{234)}00\phantom{5}\\234\overline{)876543}\\\end{array}$$

Find closest multiple of $234$ to $876$. We see that $3 \times 234 = 702$ is the nearest. Now subtract $702$ from $876$ to get reminder $174$. Add $3$ to quotient.

$$\begin{array}{l}\phantom{234)}003\phantom{6}\\234\overline{)876543}\\\phantom{234)}\underline{\phantom{}702\phantom{999}}\\\phantom{234)}174\\\end{array}$$

Use the $4^{th}$ digit $5$ from dividend $876543$

$$\begin{array}{l}\phantom{234)}003\phantom{7}\\234\overline{)876543}\\\phantom{234)}\underline{\phantom{}702\phantom{999}}\\\phantom{234)}1745\\\end{array}$$

Find closest multiple of $234$ to $1745$. We see that $7 \times 234 = 1638$ is the nearest. Now subtract $1638$ from $1745$ to get reminder $107$. Add $7$ to quotient.

$$\begin{array}{l}\phantom{234)}0037\phantom{8}\\234\overline{)876543}\\\phantom{234)}\underline{\phantom{}702\phantom{999}}\\\phantom{234)}1745\\\phantom{234)}\underline{\phantom{}1638\phantom{99}}\\\phantom{234)9}107\\\end{array}$$

Use the $5^{th}$ digit $4$ from dividend $876543$

$$\begin{array}{l}\phantom{234)}0037\phantom{9}\\234\overline{)876543}\\\phantom{234)}\underline{\phantom{}702\phantom{999}}\\\phantom{234)}1745\\\phantom{234)}\underline{\phantom{}1638\phantom{99}}\\\phantom{234)9}1074\\\end{array}$$

Find closest multiple of $234$ to $1074$. We see that $4 \times 234 = 936$ is the nearest. Now subtract $936$ from $1074$ to get reminder $138$. Add $4$ to quotient.

$$\begin{array}{l}\phantom{234)}00374\phantom{10}\\234\overline{)876543}\\\phantom{234)}\underline{\phantom{}702\phantom{999}}\\\phantom{234)}1745\\\phantom{234)}\underline{\phantom{}1638\phantom{99}}\\\phantom{234)9}1074\\\phantom{234)}\underline{\phantom{99}936\phantom{9}}\\\phantom{234)99}138\\\end{array}$$

Use the $6^{th}$ digit $3$ from dividend $876543$

$$\begin{array}{l}\phantom{234)}00374\phantom{11}\\234\overline{)876543}\\\phantom{234)}\underline{\phantom{}702\phantom{999}}\\\phantom{234)}1745\\\phantom{234)}\underline{\phantom{}1638\phantom{99}}\\\phantom{234)9}1074\\\phantom{234)}\underline{\phantom{99}936\phantom{9}}\\\phantom{234)99}1383\\\end{array}$$

Find closest multiple of $234$ to $1383$. We see that $5 \times 234 = 1170$ is the nearest. Now subtract $1170$ from $1383$ to get reminder $213$. Add $5$ to quotient.

$$\begin{array}{l}\phantom{234)}003745\phantom{12}\\234\overline{)876543}\\\phantom{234)}\underline{\phantom{}702\phantom{999}}\\\phantom{234)}1745\\\phantom{234)}\underline{\phantom{}1638\phantom{99}}\\\phantom{234)9}1074\\\phantom{234)}\underline{\phantom{99}936\phantom{9}}\\\phantom{234)99}1383\\\phantom{234)}\underline{\phantom{99}1170\phantom{}}\\\phantom{234)999}213\\\end{array}$$

Since $213$ is less than $234$, stop the division. The reminder is $213$. The topmost line $003745$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $3745$.

$$\text{Quotient: }3745$$ $$\text{Reminder: }213$$

Show Solution

Factor

$\frac{292181}{2 \cdot 3 \cdot 13} = 3745\frac{71}{78} = 3745.9102564102564$

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Steps For Long Division Method

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