Solve 823/52

$$\frac{ 823 }{ 52 }$$

Evaluate

$$\frac{823}{52}\approx 15.826923077$$

Steps For Long Division Method

Use the 1^{st} digit 8 from dividend 823

$$\begin{array}{l}\phantom{52)}\phantom{1}\\52\overline{)823}\\\end{array}$$

Since 8 is less than 52, use the next digit 2 from dividend 823 and add 0 to the quotient

$$\begin{array}{l}\phantom{52)}0\phantom{2}\\52\overline{)823}\\\end{array}$$

Use the 2^{nd} digit 2 from dividend 823

$$\begin{array}{l}\phantom{52)}0\phantom{3}\\52\overline{)823}\\\end{array}$$

Find closest multiple of 52 to 82. We see that 1 \times 52 = 52 is the nearest. Now subtract 52 from 82 to get reminder 30. Add 1 to quotient.

$$\begin{array}{l}\phantom{52)}01\phantom{4}\\52\overline{)823}\\\phantom{52)}\underline{\phantom{}52\phantom{9}}\\\phantom{52)}30\\\end{array}$$

Use the 3^{rd} digit 3 from dividend 823

$$\begin{array}{l}\phantom{52)}01\phantom{5}\\52\overline{)823}\\\phantom{52)}\underline{\phantom{}52\phantom{9}}\\\phantom{52)}303\\\end{array}$$

Find closest multiple of 52 to 303. We see that 5 \times 52 = 260 is the nearest. Now subtract 260 from 303 to get reminder 43. Add 5 to quotient.

$$\begin{array}{l}\phantom{52)}015\phantom{6}\\52\overline{)823}\\\phantom{52)}\underline{\phantom{}52\phantom{9}}\\\phantom{52)}303\\\phantom{52)}\underline{\phantom{}260\phantom{}}\\\phantom{52)9}43\\\end{array}$$

Since 43 is less than 52, stop the division. The reminder is 43. The topmost line 015 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 15.

$$\text{Quotient: }15 \text{Reminder: }43$$

Factor

$$\frac{823}{2 ^ {2} \cdot 13} = 15\frac{43}{52} = 15.826923076923077$$