How to solve a) 562580/545

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) 562580/545 | Equatix

Question

$$562580 \div 545$$

Evaluate

$\frac{112516}{109}\approx 1032.256880734$

Steps For Long Division Method

Use the $1^{st}$ digit $5$ from dividend $562580$

$$\begin{array}{l}\phantom{545)}\phantom{1}\\545\overline{)562580}\\\end{array}$$

Since $5$ is less than $545$, use the next digit $6$ from dividend $562580$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{545)}0\phantom{2}\\545\overline{)562580}\\\end{array}$$

Use the $2^{nd}$ digit $6$ from dividend $562580$

$$\begin{array}{l}\phantom{545)}0\phantom{3}\\545\overline{)562580}\\\end{array}$$

Since $56$ is less than $545$, use the next digit $2$ from dividend $562580$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{545)}00\phantom{4}\\545\overline{)562580}\\\end{array}$$

Use the $3^{rd}$ digit $2$ from dividend $562580$

$$\begin{array}{l}\phantom{545)}00\phantom{5}\\545\overline{)562580}\\\end{array}$$

Find closest multiple of $545$ to $562$. We see that $1 \times 545 = 545$ is the nearest. Now subtract $545$ from $562$ to get reminder $17$. Add $1$ to quotient.

$$\begin{array}{l}\phantom{545)}001\phantom{6}\\545\overline{)562580}\\\phantom{545)}\underline{\phantom{}545\phantom{999}}\\\phantom{545)9}17\\\end{array}$$

Use the $4^{th}$ digit $5$ from dividend $562580$

$$\begin{array}{l}\phantom{545)}001\phantom{7}\\545\overline{)562580}\\\phantom{545)}\underline{\phantom{}545\phantom{999}}\\\phantom{545)9}175\\\end{array}$$

Since $175$ is less than $545$, use the next digit $8$ from dividend $562580$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{545)}0010\phantom{8}\\545\overline{)562580}\\\phantom{545)}\underline{\phantom{}545\phantom{999}}\\\phantom{545)9}175\\\end{array}$$

Use the $5^{th}$ digit $8$ from dividend $562580$

$$\begin{array}{l}\phantom{545)}0010\phantom{9}\\545\overline{)562580}\\\phantom{545)}\underline{\phantom{}545\phantom{999}}\\\phantom{545)9}1758\\\end{array}$$

Find closest multiple of $545$ to $1758$. We see that $3 \times 545 = 1635$ is the nearest. Now subtract $1635$ from $1758$ to get reminder $123$. Add $3$ to quotient.

$$\begin{array}{l}\phantom{545)}00103\phantom{10}\\545\overline{)562580}\\\phantom{545)}\underline{\phantom{}545\phantom{999}}\\\phantom{545)9}1758\\\phantom{545)}\underline{\phantom{9}1635\phantom{9}}\\\phantom{545)99}123\\\end{array}$$

Use the $6^{th}$ digit $0$ from dividend $562580$

$$\begin{array}{l}\phantom{545)}00103\phantom{11}\\545\overline{)562580}\\\phantom{545)}\underline{\phantom{}545\phantom{999}}\\\phantom{545)9}1758\\\phantom{545)}\underline{\phantom{9}1635\phantom{9}}\\\phantom{545)99}1230\\\end{array}$$

Find closest multiple of $545$ to $1230$. We see that $2 \times 545 = 1090$ is the nearest. Now subtract $1090$ from $1230$ to get reminder $140$. Add $2$ to quotient.

$$\begin{array}{l}\phantom{545)}001032\phantom{12}\\545\overline{)562580}\\\phantom{545)}\underline{\phantom{}545\phantom{999}}\\\phantom{545)9}1758\\\phantom{545)}\underline{\phantom{9}1635\phantom{9}}\\\phantom{545)99}1230\\\phantom{545)}\underline{\phantom{99}1090\phantom{}}\\\phantom{545)999}140\\\end{array}$$

Since $140$ is less than $545$, stop the division. The reminder is $140$. The topmost line $001032$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $1032$.

$$\text{Quotient: }1032$$ $$\text{Reminder: }140$$

Show Solution

Factor

$\frac{2 ^ {2} \cdot 23 \cdot 1223}{109} = 1032\frac{28}{109} = 1032.2568807339449$

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Steps For Long Division Method

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