Solve 8192div126

$$8192 \div 126$$

Evaluate

$$\frac{4096}{63}\approx 65.015873016$$

Steps For Long Division Method

Use the 1^{st} digit 8 from dividend 8192

$$\begin{array}{l}\phantom{126)}\phantom{1}\\126\overline{)8192}\\\end{array}$$

Since 8 is less than 126, use the next digit 1 from dividend 8192 and add 0 to the quotient

$$\begin{array}{l}\phantom{126)}0\phantom{2}\\126\overline{)8192}\\\end{array}$$

Use the 2^{nd} digit 1 from dividend 8192

$$\begin{array}{l}\phantom{126)}0\phantom{3}\\126\overline{)8192}\\\end{array}$$

Since 81 is less than 126, use the next digit 9 from dividend 8192 and add 0 to the quotient

$$\begin{array}{l}\phantom{126)}00\phantom{4}\\126\overline{)8192}\\\end{array}$$

Use the 3^{rd} digit 9 from dividend 8192

$$\begin{array}{l}\phantom{126)}00\phantom{5}\\126\overline{)8192}\\\end{array}$$

Find closest multiple of 126 to 819. We see that 6 \times 126 = 756 is the nearest. Now subtract 756 from 819 to get reminder 63. Add 6 to quotient.

$$\begin{array}{l}\phantom{126)}006\phantom{6}\\126\overline{)8192}\\\phantom{126)}\underline{\phantom{}756\phantom{9}}\\\phantom{126)9}63\\\end{array}$$

Use the 4^{th} digit 2 from dividend 8192

$$\begin{array}{l}\phantom{126)}006\phantom{7}\\126\overline{)8192}\\\phantom{126)}\underline{\phantom{}756\phantom{9}}\\\phantom{126)9}632\\\end{array}$$

Find closest multiple of 126 to 632. We see that 5 \times 126 = 630 is the nearest. Now subtract 630 from 632 to get reminder 2. Add 5 to quotient.

$$\begin{array}{l}\phantom{126)}0065\phantom{8}\\126\overline{)8192}\\\phantom{126)}\underline{\phantom{}756\phantom{9}}\\\phantom{126)9}632\\\phantom{126)}\underline{\phantom{9}630\phantom{}}\\\phantom{126)999}2\\\end{array}$$

Since 2 is less than 126, stop the division. The reminder is 2. The topmost line 0065 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 65.

$$\text{Quotient: }65 \text{Reminder: }2$$

Factor

$$\frac{2 ^ {12}}{3 ^ {2} \cdot 7} = 65\frac{1}{63} = 65.01587301587301$$