# How do you divide 66,253 div 317?

Feb 4, 2017

The quotient is $209$.

#### Explanation:

(PART 1)

$66253$ is the dividend, $317$ is the divisor, and the answer is the quotient.

To make things easy and neat, we will construct the long division symbol or the division bracket.
$317 \sqrt{66253}$

First, we will divide $317$ by the first three digits of our dividend which is $662$.

317sqrt 662$53$

Now, we ask ourselves a question: "how many $317$'s can we get from $662$?". By the process of trial-and-error, we find out that we can get at least 2 $317$'s from $662$. $654$ is not "exactly $662$" but it is the closest number to $662$. Multiplying $317$ by either $1$ or $3$ will not give us the closest answer.
$317 \cdot 1 = 317$
317 * 2 = 634
$317 \cdot 3 = 951$

$2$ is the first digit of our quotient. Put $2$ on top of the dividend and align it on the third digit of the dividend. Alignment of the numbers, especially that of the quotient, is important. (Please don't mind the little dots and dashes; they are not part of the solution.)
................$2$
$317 \sqrt{66253}$

We are not done yet; that was just the first step. Multiply $2$ by $317$. The product, which is $634$, will be written underneath $662$.
................$2$
$317 \sqrt{66253}$
...........$634$_ _

Feb 4, 2017

The quotient is $209$.

#### Explanation:

(PART 2)

Now, subtract $634$ from $662$. The answer is $28$. Write it underneath $634$.
................$2$
$317 \sqrt{66253}$
...........$634$
.............$28$

Oh, and bring down the $5$ of the dividend to the difference to get the new number $285$.
................$2$
$317 \sqrt{662}$5$3$
...........$634$
.............$285$

Now, we are back to the first step. How many $317$'s can we get from $285$? The answer is "none" so we instead put $0$ next to the $2$.
................$2$0
$317 \sqrt{66253}$
...........$634$
.............285

Repeat the rest of the steps: multiplying $0$ by $317$, then subtracting $0$ from $285$, then bringing down $3$ to the difference. We repeat these steps until "all digits have been processed and no remainder is left".
................$20$
$317 \sqrt{66253}$
...........$634$
.............$285$
..................$0$_
.............2853

For the third time, repeat the rest of the steps: multiplying $9$ by $317$, then subtracting $2853$ from $2853$ to get $0$. We now know that the solution is complete to give us $209$ as the quotient.
................$209$
$317 \sqrt{66253}$
...........$634$
.............$285$
..................$0$
.............$2853$
.............$2853$

....................0

(It's a long explanation but I hope it helps greatly.)
Sources: https://en.wikipedia.org/wiki/long_division