Solve 401408div667

$$401408 \div 667$$

Evaluate

$$\frac{401408}{667}\approx 601.811094453$$

Steps For Long Division Method

Use the 1^{st} digit 4 from dividend 401408

$$\begin{array}{l}\phantom{667)}\phantom{1}\\667\overline{)401408}\\\end{array}$$

Since 4 is less than 667, use the next digit 0 from dividend 401408 and add 0 to the quotient

$$\begin{array}{l}\phantom{667)}0\phantom{2}\\667\overline{)401408}\\\end{array}$$

Use the 2^{nd} digit 0 from dividend 401408

$$\begin{array}{l}\phantom{667)}0\phantom{3}\\667\overline{)401408}\\\end{array}$$

Since 40 is less than 667, use the next digit 1 from dividend 401408 and add 0 to the quotient

$$\begin{array}{l}\phantom{667)}00\phantom{4}\\667\overline{)401408}\\\end{array}$$

Use the 3^{rd} digit 1 from dividend 401408

$$\begin{array}{l}\phantom{667)}00\phantom{5}\\667\overline{)401408}\\\end{array}$$

Since 401 is less than 667, use the next digit 4 from dividend 401408 and add 0 to the quotient

$$\begin{array}{l}\phantom{667)}000\phantom{6}\\667\overline{)401408}\\\end{array}$$

Use the 4^{th} digit 4 from dividend 401408

$$\begin{array}{l}\phantom{667)}000\phantom{7}\\667\overline{)401408}\\\end{array}$$

Find closest multiple of 667 to 4014. We see that 6 \times 667 = 4002 is the nearest. Now subtract 4002 from 4014 to get reminder 12. Add 6 to quotient.

$$\begin{array}{l}\phantom{667)}0006\phantom{8}\\667\overline{)401408}\\\phantom{667)}\underline{\phantom{}4002\phantom{99}}\\\phantom{667)99}12\\\end{array}$$

Use the 5^{th} digit 0 from dividend 401408

$$\begin{array}{l}\phantom{667)}0006\phantom{9}\\667\overline{)401408}\\\phantom{667)}\underline{\phantom{}4002\phantom{99}}\\\phantom{667)99}120\\\end{array}$$

Since 120 is less than 667, use the next digit 8 from dividend 401408 and add 0 to the quotient

$$\begin{array}{l}\phantom{667)}00060\phantom{10}\\667\overline{)401408}\\\phantom{667)}\underline{\phantom{}4002\phantom{99}}\\\phantom{667)99}120\\\end{array}$$

Use the 6^{th} digit 8 from dividend 401408

$$\begin{array}{l}\phantom{667)}00060\phantom{11}\\667\overline{)401408}\\\phantom{667)}\underline{\phantom{}4002\phantom{99}}\\\phantom{667)99}1208\\\end{array}$$

Find closest multiple of 667 to 1208. We see that 1 \times 667 = 667 is the nearest. Now subtract 667 from 1208 to get reminder 541. Add 1 to quotient.

$$\begin{array}{l}\phantom{667)}000601\phantom{12}\\667\overline{)401408}\\\phantom{667)}\underline{\phantom{}4002\phantom{99}}\\\phantom{667)99}1208\\\phantom{667)}\underline{\phantom{999}667\phantom{}}\\\phantom{667)999}541\\\end{array}$$

Since 541 is less than 667, stop the division. The reminder is 541. The topmost line 000601 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 601.

$$\text{Quotient: }601 \text{Reminder: }541$$

Factor

$$\frac{2 ^ {13} \cdot 7 ^ {2}}{23 \cdot 29} = 601\frac{541}{667} = 601.8110944527737$$