Solve 2001div1001

$$2001 \div 1001$$

Evaluate

$$\frac{2001}{1001}\approx 1.999000999$$

Steps For Long Division Method

Use the 1^{st} digit 2 from dividend 2001

$$\begin{array}{l}\phantom{1001)}\phantom{1}\\1001\overline{)2001}\\\end{array}$$

Since 2 is less than 1001, use the next digit 0 from dividend 2001 and add 0 to the quotient

$$\begin{array}{l}\phantom{1001)}0\phantom{2}\\1001\overline{)2001}\\\end{array}$$

Use the 2^{nd} digit 0 from dividend 2001

$$\begin{array}{l}\phantom{1001)}0\phantom{3}\\1001\overline{)2001}\\\end{array}$$

Since 20 is less than 1001, use the next digit 0 from dividend 2001 and add 0 to the quotient

$$\begin{array}{l}\phantom{1001)}00\phantom{4}\\1001\overline{)2001}\\\end{array}$$

Use the 3^{rd} digit 0 from dividend 2001

$$\begin{array}{l}\phantom{1001)}00\phantom{5}\\1001\overline{)2001}\\\end{array}$$

Since 200 is less than 1001, use the next digit 1 from dividend 2001 and add 0 to the quotient

$$\begin{array}{l}\phantom{1001)}000\phantom{6}\\1001\overline{)2001}\\\end{array}$$

Use the 4^{th} digit 1 from dividend 2001

$$\begin{array}{l}\phantom{1001)}000\phantom{7}\\1001\overline{)2001}\\\end{array}$$

Find closest multiple of 1001 to 2001. We see that 1 \times 1001 = 1001 is the nearest. Now subtract 1001 from 2001 to get reminder 1000. Add 1 to quotient.

$$\begin{array}{l}\phantom{1001)}0001\phantom{8}\\1001\overline{)2001}\\\phantom{1001)}\underline{\phantom{}1001\phantom{}}\\\phantom{1001)}1000\\\end{array}$$

Since 1000 is less than 1001, stop the division. The reminder is 1000. The topmost line 0001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.

$$\text{Quotient: }1 \text{Reminder: }1000$$

Factor

$$\frac{3 \cdot 23 \cdot 29}{7 \cdot 11 \cdot 13} = 1\frac{1000}{1001} = 1.999000999000999$$