Solve 100101:101

$$100101 : 101$$

Evaluate

$$\frac{100101}{101}\approx 991.099009901$$

Steps For Long Division Method

Use the 1^{st} digit 1 from dividend 100101

$$\begin{array}{l}\phantom{101)}\phantom{1}\\101\overline{)100101}\\\end{array}$$

Since 1 is less than 101, use the next digit 0 from dividend 100101 and add 0 to the quotient

$$\begin{array}{l}\phantom{101)}0\phantom{2}\\101\overline{)100101}\\\end{array}$$

Use the 2^{nd} digit 0 from dividend 100101

$$\begin{array}{l}\phantom{101)}0\phantom{3}\\101\overline{)100101}\\\end{array}$$

Since 10 is less than 101, use the next digit 0 from dividend 100101 and add 0 to the quotient

$$\begin{array}{l}\phantom{101)}00\phantom{4}\\101\overline{)100101}\\\end{array}$$

Use the 3^{rd} digit 0 from dividend 100101

$$\begin{array}{l}\phantom{101)}00\phantom{5}\\101\overline{)100101}\\\end{array}$$

Since 100 is less than 101, use the next digit 1 from dividend 100101 and add 0 to the quotient

$$\begin{array}{l}\phantom{101)}000\phantom{6}\\101\overline{)100101}\\\end{array}$$

Use the 4^{th} digit 1 from dividend 100101

$$\begin{array}{l}\phantom{101)}000\phantom{7}\\101\overline{)100101}\\\end{array}$$

Find closest multiple of 101 to 1001. We see that 9 \times 101 = 909 is the nearest. Now subtract 909 from 1001 to get reminder 92. Add 9 to quotient.

$$\begin{array}{l}\phantom{101)}0009\phantom{8}\\101\overline{)100101}\\\phantom{101)}\underline{\phantom{9}909\phantom{99}}\\\phantom{101)99}92\\\end{array}$$

Use the 5^{th} digit 0 from dividend 100101

$$\begin{array}{l}\phantom{101)}0009\phantom{9}\\101\overline{)100101}\\\phantom{101)}\underline{\phantom{9}909\phantom{99}}\\\phantom{101)99}920\\\end{array}$$

Find closest multiple of 101 to 920. We see that 9 \times 101 = 909 is the nearest. Now subtract 909 from 920 to get reminder 11. Add 9 to quotient.

$$\begin{array}{l}\phantom{101)}00099\phantom{10}\\101\overline{)100101}\\\phantom{101)}\underline{\phantom{9}909\phantom{99}}\\\phantom{101)99}920\\\phantom{101)}\underline{\phantom{99}909\phantom{9}}\\\phantom{101)999}11\\\end{array}$$

Use the 6^{th} digit 1 from dividend 100101

$$\begin{array}{l}\phantom{101)}00099\phantom{11}\\101\overline{)100101}\\\phantom{101)}\underline{\phantom{9}909\phantom{99}}\\\phantom{101)99}920\\\phantom{101)}\underline{\phantom{99}909\phantom{9}}\\\phantom{101)999}111\\\end{array}$$

Find closest multiple of 101 to 111. We see that 1 \times 101 = 101 is the nearest. Now subtract 101 from 111 to get reminder 10. Add 1 to quotient.

$$\begin{array}{l}\phantom{101)}000991\phantom{12}\\101\overline{)100101}\\\phantom{101)}\underline{\phantom{9}909\phantom{99}}\\\phantom{101)99}920\\\phantom{101)}\underline{\phantom{99}909\phantom{9}}\\\phantom{101)999}111\\\phantom{101)}\underline{\phantom{999}101\phantom{}}\\\phantom{101)9999}10\\\end{array}$$

Since 10 is less than 101, stop the division. The reminder is 10. The topmost line 000991 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 991.

$$\text{Quotient: }991 \text{Reminder: }10$$

Factor

$$\frac{3 \cdot 61 \cdot 547}{101} = 991\frac{10}{101} = 991.0990099009902$$