Is there a way to tell - for example - how many $60$s are there in a number that cannot be divided by $60$, like $183$? I know that we should remove all numbers after the decimal point but how can we tell this mathematically?
2026-04-24 15:53:27.1777046007
Finding how many times one number fits into the other
62.5k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
It is still unclear whether you are looking for a trick, a formula, an algorithm, or a mathematical definition, so I will provide all four.
Trick: Probably the easiest way to do this by hand is do long division on $183 / 60$ but throw away the remainder (or remove all the numbers after the decimal point, if you prefer).
Formula: This is generally written $\left\lfloor \frac{183}{60} \right\rfloor$. Here $\lfloor x \rfloor$ is called the "floor" of $x$ and means the greatest integer less than or equal to $x$.
Algorithm: This is called the Division Algorithm (as was mentioned by Sigur in the comments). Basically, you subtract 60 from 183 until you get something on the interval [0, 60), and you count the number of times you subtracted 60 to get the answer.
Definition: Let $a$ and $b$ be integers. The integer quotient of $a$ and $b$ is defined to be the largest integer $k$ such that $a > bk$. (Note that this is well-defined if and only if $b > 0$). In the case of 183 and 60, we want the largest integer $k$ such that $183 > 60k$.