What are the divisors of 60?

To know what are the divisors of 60, It is convenient to realize that they are also called "factors" of a number that, in the specific case at hand, is 60.

Its divisors are 1,2,3,4,5,6, 10, 12, 15, 20, 30 and 60, placing them in a strict order. Let us also note that the least common divisor is 1, while the highest is 60.

The mathematical explanation why these are the divisors of 60

Before any consideration, and in order to carry a logical sequence in the explanation, it is advisable to analyze the definitions of "Factor", Multiple "and" Divisor ".

Two numbers are factors of a specific number, if your product is the number itself. For example, 4 x 3 is equal to 12.

So 4 and 3 are factors of 12 for obvious reasons. In other words but in the same conceptual direction, the number is the multiple of a factor.

In the case of the example that we have been developing, 12 is a multiple of 4 and, also, of 3. But, yes, the same 12 can be a multiple of other combinations of numbers, such as, for example, 6 and 2, because 6 x 2 equals 12.

Also, each factor is a divisor of the number. Let's see examples, for a better understanding

Let's go back to the initial question:what are the divisors of 60? According to what has just been “subtitled”, each of the factors of 60 that we have alluded to are, at the same time, divisors.

Let's see, now, a more detailed explanation about what is called the "General Property" when the natural numbers are the same "Universal Set".

"A" is a factor of "B", as long as this equation exists: B = AK, where A, B and K are constituted in a subset (or "group", to put it in more understandable terms) of the "Universal Set" of natural numbers.

In the same way, we have that B is a multiple of A, provided that B = AK, that is, if B is equal to the multiplication in A x K.

Let's “play around” with the numbers to better understand the divisors of 60

So 5 x 8 = 40 right? Therefore, 5 and 8 are factors of 40, due to the explanations already formulated.

Now, since 5 x 8 = 40, the latter is a multiple of 5 and is a multiple of 8 as well. Therefore, 5 and 8 are, in addition to multiples of 40, divisors of the same.

To find out what the divisors of 60 are and their mathematical reason, let's move this example to the number 60 itself. 

It is evident that 12 x 5 = 60. It follows that both 12 and 5 are factors of 60 (remember that 5 and 12 are on the list in the introductory section).

Therefore, 60 is a multiple of 5 and, also, of 12. As a consequence, and starting from the mathematical principle that says that multiples are, at the same time, divisors of a number, 5 and 12 are divisors of 60.

References

1. Factors, Multiples and Divisors (No year). Recovered from web.mnstate.edu
2. Times Table (No year). Factors of 60. Recovered from times-table.net
3. Lavrov, Misha (2013). Number Theory. Theory of Divisors. Recovered from math.cmu.edu
4. Mathematics 1st That (No year). Multiples and Divisors. Recovered from recursostic.educacion.es
5. Arrondo, Enrique (2009). Notes on Elementary Number Theory. Recovered from mat.ucm.es.