Solve 1000101:101

$$1000101 : 101$$

Evaluate

$$\frac{1000101}{101}\approx 9901.99009901$$

Steps For Long Division Method

Use the 1^{st} digit 1 from dividend 1000101

$$\begin{array}{l}\phantom{101)}\phantom{1}\\101\overline{)1000101}\\\end{array}$$

Since 1 is less than 101, use the next digit 0 from dividend 1000101 and add 0 to the quotient

$$\begin{array}{l}\phantom{101)}0\phantom{2}\\101\overline{)1000101}\\\end{array}$$

Use the 2^{nd} digit 0 from dividend 1000101

$$\begin{array}{l}\phantom{101)}0\phantom{3}\\101\overline{)1000101}\\\end{array}$$

Since 10 is less than 101, use the next digit 0 from dividend 1000101 and add 0 to the quotient

$$\begin{array}{l}\phantom{101)}00\phantom{4}\\101\overline{)1000101}\\\end{array}$$

Use the 3^{rd} digit 0 from dividend 1000101

$$\begin{array}{l}\phantom{101)}00\phantom{5}\\101\overline{)1000101}\\\end{array}$$

Since 100 is less than 101, use the next digit 0 from dividend 1000101 and add 0 to the quotient

$$\begin{array}{l}\phantom{101)}000\phantom{6}\\101\overline{)1000101}\\\end{array}$$

Use the 4^{th} digit 0 from dividend 1000101

$$\begin{array}{l}\phantom{101)}000\phantom{7}\\101\overline{)1000101}\\\end{array}$$

Find closest multiple of 101 to 1000. We see that 9 \times 101 = 909 is the nearest. Now subtract 909 from 1000 to get reminder 91. Add 9 to quotient.

$$\begin{array}{l}\phantom{101)}0009\phantom{8}\\101\overline{)1000101}\\\phantom{101)}\underline{\phantom{9}909\phantom{999}}\\\phantom{101)99}91\\\end{array}$$

Use the 5^{th} digit 1 from dividend 1000101

$$\begin{array}{l}\phantom{101)}0009\phantom{9}\\101\overline{)1000101}\\\phantom{101)}\underline{\phantom{9}909\phantom{999}}\\\phantom{101)99}911\\\end{array}$$

Find closest multiple of 101 to 911. We see that 9 \times 101 = 909 is the nearest. Now subtract 909 from 911 to get reminder 2. Add 9 to quotient.

$$\begin{array}{l}\phantom{101)}00099\phantom{10}\\101\overline{)1000101}\\\phantom{101)}\underline{\phantom{9}909\phantom{999}}\\\phantom{101)99}911\\\phantom{101)}\underline{\phantom{99}909\phantom{99}}\\\phantom{101)9999}2\\\end{array}$$

Use the 6^{th} digit 0 from dividend 1000101

$$\begin{array}{l}\phantom{101)}00099\phantom{11}\\101\overline{)1000101}\\\phantom{101)}\underline{\phantom{9}909\phantom{999}}\\\phantom{101)99}911\\\phantom{101)}\underline{\phantom{99}909\phantom{99}}\\\phantom{101)9999}20\\\end{array}$$

Since 20 is less than 101, use the next digit 1 from dividend 1000101 and add 0 to the quotient

$$\begin{array}{l}\phantom{101)}000990\phantom{12}\\101\overline{)1000101}\\\phantom{101)}\underline{\phantom{9}909\phantom{999}}\\\phantom{101)99}911\\\phantom{101)}\underline{\phantom{99}909\phantom{99}}\\\phantom{101)9999}20\\\end{array}$$

Use the 7^{th} digit 1 from dividend 1000101

$$\begin{array}{l}\phantom{101)}000990\phantom{13}\\101\overline{)1000101}\\\phantom{101)}\underline{\phantom{9}909\phantom{999}}\\\phantom{101)99}911\\\phantom{101)}\underline{\phantom{99}909\phantom{99}}\\\phantom{101)9999}201\\\end{array}$$

Find closest multiple of 101 to 201. We see that 1 \times 101 = 101 is the nearest. Now subtract 101 from 201 to get reminder 100. Add 1 to quotient.

$$\begin{array}{l}\phantom{101)}0009901\phantom{14}\\101\overline{)1000101}\\\phantom{101)}\underline{\phantom{9}909\phantom{999}}\\\phantom{101)99}911\\\phantom{101)}\underline{\phantom{99}909\phantom{99}}\\\phantom{101)9999}201\\\phantom{101)}\underline{\phantom{9999}101\phantom{}}\\\phantom{101)9999}100\\\end{array}$$

Since 100 is less than 101, stop the division. The reminder is 100. The topmost line 0009901 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9901.

$$\text{Quotient: }9901 \text{Reminder: }100$$

Factor

$$\frac{3 \cdot 333367}{101} = 9901\frac{100}{101} = 9901.990099009901$$