**The maximum is the largest value within a group of numbers. That is, having a set C, and an element x that belongs to it (x ∈ C), x is the maximum element of C if any other element of that set is less than or equal to x.**

In formal terms, all elements (n) that belong to C have a value lower than x (n ≤ x).

For example, if we analyze historical data we can calculate the maximum exchange rate that the dollar has had against the euro in the last ten years.

Another case is when an estimate is made, for example, of the maximum or highest temperature that a city will register during a given day, which could be 30 degrees Celsius on a summer day.

Another practical example could be that of a person who keeps track of his finances and finds the following expenses in August:

- August 02: 30 euros
- August 15: 50 euros
- August 17: 100 euros
- August 22: 40 euros
- August 29: 132 euros
- August 31: 54 euros

Taking into account the data presented, it is concluded that the maximum daily expenditure registered by the person is 132 euros in the month of August.

It should be noted that the maximum can be set as a rule, that is, an upper limit that cannot be exceeded. For example, when on a highway the maximum speed limit is 90 kilometers per hour.

## Greatest common divisor

The greatest common divisor (GCF) is the largest number by which two or more numbers can be divided. This, without leaving any residue.

That is, the GCF is the highest figure by which a set of numbers can be divided, resulting in a whole number.

It should be noted that the numbers on which the GCF is calculated must be nonzero.

To explain it better, let’s look at an example. Suppose we have 35 and 15. Thus, we observe what the divisors of each are:

- Divisors of 35 → 35,7,5,1
- Divisors of 15 → 15,5,3,1

Therefore, the greatest common factor of 35 and 15 is 5.

Numeric sets