Solve 2002/2000

$$\frac { 2002 } { 2000 }$$

Evaluate

$$\frac{1001}{1000}=1.001$$

Steps For Long Division Method

Use the 1^{st} digit 2 from dividend 2002

$$\begin{array}{l}\phantom{2000)}\phantom{1}\\2000\overline{)2002}\\\end{array}$$

Since 2 is less than 2000, use the next digit 0 from dividend 2002 and add 0 to the quotient

$$\begin{array}{l}\phantom{2000)}0\phantom{2}\\2000\overline{)2002}\\\end{array}$$

Use the 2^{nd} digit 0 from dividend 2002

$$\begin{array}{l}\phantom{2000)}0\phantom{3}\\2000\overline{)2002}\\\end{array}$$

Since 20 is less than 2000, use the next digit 0 from dividend 2002 and add 0 to the quotient

$$\begin{array}{l}\phantom{2000)}00\phantom{4}\\2000\overline{)2002}\\\end{array}$$

Use the 3^{rd} digit 0 from dividend 2002

$$\begin{array}{l}\phantom{2000)}00\phantom{5}\\2000\overline{)2002}\\\end{array}$$

Since 200 is less than 2000, use the next digit 2 from dividend 2002 and add 0 to the quotient

$$\begin{array}{l}\phantom{2000)}000\phantom{6}\\2000\overline{)2002}\\\end{array}$$

Use the 4^{th} digit 2 from dividend 2002

$$\begin{array}{l}\phantom{2000)}000\phantom{7}\\2000\overline{)2002}\\\end{array}$$

Find closest multiple of 2000 to 2002. We see that 1 \times 2000 = 2000 is the nearest. Now subtract 2000 from 2002 to get reminder 2. Add 1 to quotient.

$$\begin{array}{l}\phantom{2000)}0001\phantom{8}\\2000\overline{)2002}\\\phantom{2000)}\underline{\phantom{}2000\phantom{}}\\\phantom{2000)999}2\\\end{array}$$

Since 2 is less than 2000, stop the division. The reminder is 2. The topmost line 0001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.

$$\text{Quotient: }1 \text{Reminder: }2$$

Factor

$$\frac{7 \cdot 11 \cdot 13}{2 ^ {3} \cdot 5 ^ {3}} = 1\frac{1}{1000} = 1.001$$