How to solve 538913/366

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 538913/366 | Equatix

Question

$$538913/366$$

Evaluate

$\frac{538913}{366}\approx 1472.43989071$

Steps For Long Division Method

Use the $1^{st}$ digit $5$ from dividend $538913$

$$\begin{array}{l}\phantom{366)}\phantom{1}\\366\overline{)538913}\\\end{array}$$

Since $5$ is less than $366$, use the next digit $3$ from dividend $538913$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{366)}0\phantom{2}\\366\overline{)538913}\\\end{array}$$

Use the $2^{nd}$ digit $3$ from dividend $538913$

$$\begin{array}{l}\phantom{366)}0\phantom{3}\\366\overline{)538913}\\\end{array}$$

Since $53$ is less than $366$, use the next digit $8$ from dividend $538913$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{366)}00\phantom{4}\\366\overline{)538913}\\\end{array}$$

Use the $3^{rd}$ digit $8$ from dividend $538913$

$$\begin{array}{l}\phantom{366)}00\phantom{5}\\366\overline{)538913}\\\end{array}$$

Find closest multiple of $366$ to $538$. We see that $1 \times 366 = 366$ is the nearest. Now subtract $366$ from $538$ to get reminder $172$. Add $1$ to quotient.

$$\begin{array}{l}\phantom{366)}001\phantom{6}\\366\overline{)538913}\\\phantom{366)}\underline{\phantom{}366\phantom{999}}\\\phantom{366)}172\\\end{array}$$

Use the $4^{th}$ digit $9$ from dividend $538913$

$$\begin{array}{l}\phantom{366)}001\phantom{7}\\366\overline{)538913}\\\phantom{366)}\underline{\phantom{}366\phantom{999}}\\\phantom{366)}1729\\\end{array}$$

Find closest multiple of $366$ to $1729$. We see that $4 \times 366 = 1464$ is the nearest. Now subtract $1464$ from $1729$ to get reminder $265$. Add $4$ to quotient.

$$\begin{array}{l}\phantom{366)}0014\phantom{8}\\366\overline{)538913}\\\phantom{366)}\underline{\phantom{}366\phantom{999}}\\\phantom{366)}1729\\\phantom{366)}\underline{\phantom{}1464\phantom{99}}\\\phantom{366)9}265\\\end{array}$$

Use the $5^{th}$ digit $1$ from dividend $538913$

$$\begin{array}{l}\phantom{366)}0014\phantom{9}\\366\overline{)538913}\\\phantom{366)}\underline{\phantom{}366\phantom{999}}\\\phantom{366)}1729\\\phantom{366)}\underline{\phantom{}1464\phantom{99}}\\\phantom{366)9}2651\\\end{array}$$

Find closest multiple of $366$ to $2651$. We see that $7 \times 366 = 2562$ is the nearest. Now subtract $2562$ from $2651$ to get reminder $89$. Add $7$ to quotient.

$$\begin{array}{l}\phantom{366)}00147\phantom{10}\\366\overline{)538913}\\\phantom{366)}\underline{\phantom{}366\phantom{999}}\\\phantom{366)}1729\\\phantom{366)}\underline{\phantom{}1464\phantom{99}}\\\phantom{366)9}2651\\\phantom{366)}\underline{\phantom{9}2562\phantom{9}}\\\phantom{366)999}89\\\end{array}$$

Use the $6^{th}$ digit $3$ from dividend $538913$

$$\begin{array}{l}\phantom{366)}00147\phantom{11}\\366\overline{)538913}\\\phantom{366)}\underline{\phantom{}366\phantom{999}}\\\phantom{366)}1729\\\phantom{366)}\underline{\phantom{}1464\phantom{99}}\\\phantom{366)9}2651\\\phantom{366)}\underline{\phantom{9}2562\phantom{9}}\\\phantom{366)999}893\\\end{array}$$

Find closest multiple of $366$ to $893$. We see that $2 \times 366 = 732$ is the nearest. Now subtract $732$ from $893$ to get reminder $161$. Add $2$ to quotient.

$$\begin{array}{l}\phantom{366)}001472\phantom{12}\\366\overline{)538913}\\\phantom{366)}\underline{\phantom{}366\phantom{999}}\\\phantom{366)}1729\\\phantom{366)}\underline{\phantom{}1464\phantom{99}}\\\phantom{366)9}2651\\\phantom{366)}\underline{\phantom{9}2562\phantom{9}}\\\phantom{366)999}893\\\phantom{366)}\underline{\phantom{999}732\phantom{}}\\\phantom{366)999}161\\\end{array}$$

Since $161$ is less than $366$, stop the division. The reminder is $161$. The topmost line $001472$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $1472$.

$$\text{Quotient: }1472$$ $$\text{Reminder: }161$$

Show Solution

Factor

$\frac{23 \cdot 23431}{2 \cdot 3 \cdot 61} = 1472\frac{161}{366} = 1472.4398907103825$

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Steps For Long Division Method

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