Solve (1234567890)/(369) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{ 1234567890 }{ 369 }$$

Evaluate

$\frac{137174210}{41}\approx 3345712.43902439$

Steps For Long Division Method

Use the $1^{st}$ digit $1$ from dividend $1234567890$

$$\begin{array}{l}\phantom{369)}\phantom{1}\\369\overline{)1234567890}\\\end{array}$$

Since $1$ is less than $369$, use the next digit $2$ from dividend $1234567890$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{369)}0\phantom{2}\\369\overline{)1234567890}\\\end{array}$$

Use the $2^{nd}$ digit $2$ from dividend $1234567890$

$$\begin{array}{l}\phantom{369)}0\phantom{3}\\369\overline{)1234567890}\\\end{array}$$

Since $12$ is less than $369$, use the next digit $3$ from dividend $1234567890$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{369)}00\phantom{4}\\369\overline{)1234567890}\\\end{array}$$

Use the $3^{rd}$ digit $3$ from dividend $1234567890$

$$\begin{array}{l}\phantom{369)}00\phantom{5}\\369\overline{)1234567890}\\\end{array}$$

Since $123$ is less than $369$, use the next digit $4$ from dividend $1234567890$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{369)}000\phantom{6}\\369\overline{)1234567890}\\\end{array}$$

Use the $4^{th}$ digit $4$ from dividend $1234567890$

$$\begin{array}{l}\phantom{369)}000\phantom{7}\\369\overline{)1234567890}\\\end{array}$$

Find closest multiple of $369$ to $1234$. We see that $3 \times 369 = 1107$ is the nearest. Now subtract $1107$ from $1234$ to get reminder $127$. Add $3$ to quotient.

$$\begin{array}{l}\phantom{369)}0003\phantom{8}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}127\\\end{array}$$

Use the $5^{th}$ digit $5$ from dividend $1234567890$

$$\begin{array}{l}\phantom{369)}0003\phantom{9}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}1275\\\end{array}$$

Find closest multiple of $369$ to $1275$. We see that $3 \times 369 = 1107$ is the nearest. Now subtract $1107$ from $1275$ to get reminder $168$. Add $3$ to quotient.

$$\begin{array}{l}\phantom{369)}00033\phantom{10}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}1275\\\phantom{369)}\underline{\phantom{9}1107\phantom{99999}}\\\phantom{369)99}168\\\end{array}$$

Use the $6^{th}$ digit $6$ from dividend $1234567890$

$$\begin{array}{l}\phantom{369)}00033\phantom{11}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}1275\\\phantom{369)}\underline{\phantom{9}1107\phantom{99999}}\\\phantom{369)99}1686\\\end{array}$$

Find closest multiple of $369$ to $1686$. We see that $4 \times 369 = 1476$ is the nearest. Now subtract $1476$ from $1686$ to get reminder $210$. Add $4$ to quotient.

$$\begin{array}{l}\phantom{369)}000334\phantom{12}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}1275\\\phantom{369)}\underline{\phantom{9}1107\phantom{99999}}\\\phantom{369)99}1686\\\phantom{369)}\underline{\phantom{99}1476\phantom{9999}}\\\phantom{369)999}210\\\end{array}$$

Use the $7^{th}$ digit $7$ from dividend $1234567890$

$$\begin{array}{l}\phantom{369)}000334\phantom{13}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}1275\\\phantom{369)}\underline{\phantom{9}1107\phantom{99999}}\\\phantom{369)99}1686\\\phantom{369)}\underline{\phantom{99}1476\phantom{9999}}\\\phantom{369)999}2107\\\end{array}$$

Find closest multiple of $369$ to $2107$. We see that $5 \times 369 = 1845$ is the nearest. Now subtract $1845$ from $2107$ to get reminder $262$. Add $5$ to quotient.

$$\begin{array}{l}\phantom{369)}0003345\phantom{14}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}1275\\\phantom{369)}\underline{\phantom{9}1107\phantom{99999}}\\\phantom{369)99}1686\\\phantom{369)}\underline{\phantom{99}1476\phantom{9999}}\\\phantom{369)999}2107\\\phantom{369)}\underline{\phantom{999}1845\phantom{999}}\\\phantom{369)9999}262\\\end{array}$$

Use the $8^{th}$ digit $8$ from dividend $1234567890$

$$\begin{array}{l}\phantom{369)}0003345\phantom{15}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}1275\\\phantom{369)}\underline{\phantom{9}1107\phantom{99999}}\\\phantom{369)99}1686\\\phantom{369)}\underline{\phantom{99}1476\phantom{9999}}\\\phantom{369)999}2107\\\phantom{369)}\underline{\phantom{999}1845\phantom{999}}\\\phantom{369)9999}2628\\\end{array}$$

Find closest multiple of $369$ to $2628$. We see that $7 \times 369 = 2583$ is the nearest. Now subtract $2583$ from $2628$ to get reminder $45$. Add $7$ to quotient.

$$\begin{array}{l}\phantom{369)}00033457\phantom{16}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}1275\\\phantom{369)}\underline{\phantom{9}1107\phantom{99999}}\\\phantom{369)99}1686\\\phantom{369)}\underline{\phantom{99}1476\phantom{9999}}\\\phantom{369)999}2107\\\phantom{369)}\underline{\phantom{999}1845\phantom{999}}\\\phantom{369)9999}2628\\\phantom{369)}\underline{\phantom{9999}2583\phantom{99}}\\\phantom{369)999999}45\\\end{array}$$

Use the $9^{th}$ digit $9$ from dividend $1234567890$

$$\begin{array}{l}\phantom{369)}00033457\phantom{17}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}1275\\\phantom{369)}\underline{\phantom{9}1107\phantom{99999}}\\\phantom{369)99}1686\\\phantom{369)}\underline{\phantom{99}1476\phantom{9999}}\\\phantom{369)999}2107\\\phantom{369)}\underline{\phantom{999}1845\phantom{999}}\\\phantom{369)9999}2628\\\phantom{369)}\underline{\phantom{9999}2583\phantom{99}}\\\phantom{369)999999}459\\\end{array}$$

Find closest multiple of $369$ to $459$. We see that $1 \times 369 = 369$ is the nearest. Now subtract $369$ from $459$ to get reminder $90$. Add $1$ to quotient.

$$\begin{array}{l}\phantom{369)}000334571\phantom{18}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}1275\\\phantom{369)}\underline{\phantom{9}1107\phantom{99999}}\\\phantom{369)99}1686\\\phantom{369)}\underline{\phantom{99}1476\phantom{9999}}\\\phantom{369)999}2107\\\phantom{369)}\underline{\phantom{999}1845\phantom{999}}\\\phantom{369)9999}2628\\\phantom{369)}\underline{\phantom{9999}2583\phantom{99}}\\\phantom{369)999999}459\\\phantom{369)}\underline{\phantom{999999}369\phantom{9}}\\\phantom{369)9999999}90\\\end{array}$$

Use the $10^{th}$ digit $0$ from dividend $1234567890$

$$\begin{array}{l}\phantom{369)}000334571\phantom{19}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}1275\\\phantom{369)}\underline{\phantom{9}1107\phantom{99999}}\\\phantom{369)99}1686\\\phantom{369)}\underline{\phantom{99}1476\phantom{9999}}\\\phantom{369)999}2107\\\phantom{369)}\underline{\phantom{999}1845\phantom{999}}\\\phantom{369)9999}2628\\\phantom{369)}\underline{\phantom{9999}2583\phantom{99}}\\\phantom{369)999999}459\\\phantom{369)}\underline{\phantom{999999}369\phantom{9}}\\\phantom{369)9999999}900\\\end{array}$$

Find closest multiple of $369$ to $900$. We see that $2 \times 369 = 738$ is the nearest. Now subtract $738$ from $900$ to get reminder $162$. Add $2$ to quotient.

$$\begin{array}{l}\phantom{369)}0003345712\phantom{20}\\369\overline{)1234567890}\\\phantom{369)}\underline{\phantom{}1107\phantom{999999}}\\\phantom{369)9}1275\\\phantom{369)}\underline{\phantom{9}1107\phantom{99999}}\\\phantom{369)99}1686\\\phantom{369)}\underline{\phantom{99}1476\phantom{9999}}\\\phantom{369)999}2107\\\phantom{369)}\underline{\phantom{999}1845\phantom{999}}\\\phantom{369)9999}2628\\\phantom{369)}\underline{\phantom{9999}2583\phantom{99}}\\\phantom{369)999999}459\\\phantom{369)}\underline{\phantom{999999}369\phantom{9}}\\\phantom{369)9999999}900\\\phantom{369)}\underline{\phantom{9999999}738\phantom{}}\\\phantom{369)9999999}162\\\end{array}$$

Since $162$ is less than $369$, stop the division. The reminder is $162$. The topmost line $0003345712$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $3345712$.

$$\text{Quotient: }3345712$$ $$\text{Reminder: }162$$

Factor

$\frac{2 \cdot 5 \cdot 3607 \cdot 3803}{41} = 3345712\frac{18}{41} = 3345712.43902439$