Solve 1010010/1100

$$\frac { 1010010 } { 1100 }$$

Evaluate

$$\frac{101001}{110}\approx 918.190909091$$

Steps For Long Division Method

Use the 1^{st} digit 1 from dividend 1010010

$$\begin{array}{l}\phantom{1100)}\phantom{1}\\1100\overline{)1010010}\\\end{array}$$

Since 1 is less than 1100, use the next digit 0 from dividend 1010010 and add 0 to the quotient

$$\begin{array}{l}\phantom{1100)}0\phantom{2}\\1100\overline{)1010010}\\\end{array}$$

Use the 2^{nd} digit 0 from dividend 1010010

$$\begin{array}{l}\phantom{1100)}0\phantom{3}\\1100\overline{)1010010}\\\end{array}$$

Since 10 is less than 1100, use the next digit 1 from dividend 1010010 and add 0 to the quotient

$$\begin{array}{l}\phantom{1100)}00\phantom{4}\\1100\overline{)1010010}\\\end{array}$$

Use the 3^{rd} digit 1 from dividend 1010010

$$\begin{array}{l}\phantom{1100)}00\phantom{5}\\1100\overline{)1010010}\\\end{array}$$

Since 101 is less than 1100, use the next digit 0 from dividend 1010010 and add 0 to the quotient

$$\begin{array}{l}\phantom{1100)}000\phantom{6}\\1100\overline{)1010010}\\\end{array}$$

Use the 4^{th} digit 0 from dividend 1010010

$$\begin{array}{l}\phantom{1100)}000\phantom{7}\\1100\overline{)1010010}\\\end{array}$$

Since 1010 is less than 1100, use the next digit 0 from dividend 1010010 and add 0 to the quotient

$$\begin{array}{l}\phantom{1100)}0000\phantom{8}\\1100\overline{)1010010}\\\end{array}$$

Use the 5^{th} digit 0 from dividend 1010010

$$\begin{array}{l}\phantom{1100)}0000\phantom{9}\\1100\overline{)1010010}\\\end{array}$$

Find closest multiple of 1100 to 10100. We see that 9 \times 1100 = 9900 is the nearest. Now subtract 9900 from 10100 to get reminder 200. Add 9 to quotient.

$$\begin{array}{l}\phantom{1100)}00009\phantom{10}\\1100\overline{)1010010}\\\phantom{1100)}\underline{\phantom{9}9900\phantom{99}}\\\phantom{1100)99}200\\\end{array}$$

Use the 6^{th} digit 1 from dividend 1010010

$$\begin{array}{l}\phantom{1100)}00009\phantom{11}\\1100\overline{)1010010}\\\phantom{1100)}\underline{\phantom{9}9900\phantom{99}}\\\phantom{1100)99}2001\\\end{array}$$

Find closest multiple of 1100 to 2001. We see that 1 \times 1100 = 1100 is the nearest. Now subtract 1100 from 2001 to get reminder 901. Add 1 to quotient.

$$\begin{array}{l}\phantom{1100)}000091\phantom{12}\\1100\overline{)1010010}\\\phantom{1100)}\underline{\phantom{9}9900\phantom{99}}\\\phantom{1100)99}2001\\\phantom{1100)}\underline{\phantom{99}1100\phantom{9}}\\\phantom{1100)999}901\\\end{array}$$

Use the 7^{th} digit 0 from dividend 1010010

$$\begin{array}{l}\phantom{1100)}000091\phantom{13}\\1100\overline{)1010010}\\\phantom{1100)}\underline{\phantom{9}9900\phantom{99}}\\\phantom{1100)99}2001\\\phantom{1100)}\underline{\phantom{99}1100\phantom{9}}\\\phantom{1100)999}9010\\\end{array}$$

Find closest multiple of 1100 to 9010. We see that 8 \times 1100 = 8800 is the nearest. Now subtract 8800 from 9010 to get reminder 210. Add 8 to quotient.

$$\begin{array}{l}\phantom{1100)}0000918\phantom{14}\\1100\overline{)1010010}\\\phantom{1100)}\underline{\phantom{9}9900\phantom{99}}\\\phantom{1100)99}2001\\\phantom{1100)}\underline{\phantom{99}1100\phantom{9}}\\\phantom{1100)999}9010\\\phantom{1100)}\underline{\phantom{999}8800\phantom{}}\\\phantom{1100)9999}210\\\end{array}$$

Since 210 is less than 1100, stop the division. The reminder is 210. The topmost line 0000918 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 918.

$$\text{Quotient: }918 \text{Reminder: }210$$

Factor

$$\frac{3 \cdot 131 \cdot 257}{2 \cdot 5 \cdot 11} = 918\frac{21}{110} = 918.1909090909091$$