Solve 2048div105

$$2048 \div 105$$

Evaluate

$$\frac{2048}{105}\approx 19.504761905$$

Steps For Long Division Method

Use the 1^{st} digit 2 from dividend 2048

$$\begin{array}{l}\phantom{105)}\phantom{1}\\105\overline{)2048}\\\end{array}$$

Since 2 is less than 105, use the next digit 0 from dividend 2048 and add 0 to the quotient

$$\begin{array}{l}\phantom{105)}0\phantom{2}\\105\overline{)2048}\\\end{array}$$

Use the 2^{nd} digit 0 from dividend 2048

$$\begin{array}{l}\phantom{105)}0\phantom{3}\\105\overline{)2048}\\\end{array}$$

Since 20 is less than 105, use the next digit 4 from dividend 2048 and add 0 to the quotient

$$\begin{array}{l}\phantom{105)}00\phantom{4}\\105\overline{)2048}\\\end{array}$$

Use the 3^{rd} digit 4 from dividend 2048

$$\begin{array}{l}\phantom{105)}00\phantom{5}\\105\overline{)2048}\\\end{array}$$

Find closest multiple of 105 to 204. We see that 1 \times 105 = 105 is the nearest. Now subtract 105 from 204 to get reminder 99. Add 1 to quotient.

$$\begin{array}{l}\phantom{105)}001\phantom{6}\\105\overline{)2048}\\\phantom{105)}\underline{\phantom{}105\phantom{9}}\\\phantom{105)9}99\\\end{array}$$

Use the 4^{th} digit 8 from dividend 2048

$$\begin{array}{l}\phantom{105)}001\phantom{7}\\105\overline{)2048}\\\phantom{105)}\underline{\phantom{}105\phantom{9}}\\\phantom{105)9}998\\\end{array}$$

Find closest multiple of 105 to 998. We see that 9 \times 105 = 945 is the nearest. Now subtract 945 from 998 to get reminder 53. Add 9 to quotient.

$$\begin{array}{l}\phantom{105)}0019\phantom{8}\\105\overline{)2048}\\\phantom{105)}\underline{\phantom{}105\phantom{9}}\\\phantom{105)9}998\\\phantom{105)}\underline{\phantom{9}945\phantom{}}\\\phantom{105)99}53\\\end{array}$$

Since 53 is less than 105, stop the division. The reminder is 53. The topmost line 0019 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 19.

$$\text{Quotient: }19 \text{Reminder: }53$$

Factor

$$\frac{2 ^ {11}}{3 \cdot 5 \cdot 7} = 19\frac{53}{105} = 19.504761904761907$$