# Divisible or divisible, what is the correct form of this word?

Derivative works and especially some adjectives that are derived from nouns are not always regular in Spanish and that is why they tend to generate doubts when writing them, as happens with the question: is it written ** divisible or divisible**?

In this case, there is only one answer and that is that the correct form is divisible, with an S and not with a D. Now we are going to see the meaning of this word, as well as examples of its use so that you always remember it.

## Divisible

This is the correct way to write this word, which is used to refer to the possibility or ability of something to be divided or divided. Like the noun division, from which it comes, it must always be written with S. On the other hand, the antonym of this word is indivisible, which must also be written with S.

#### Examples:

- Juan and Marta have been together for years, they are already an indivisible couple.
- This number is not divisible without using decimal numbers.
- Formerly it was believed that the atom was indivisible.
- This dish is expensive because it is divisible between two people.
- This toy is divisible into pieces that you can also play with.

## Divisible

Even though one might think that since the verb to *divide* is written with D, then the correct form should be “divisible”, in reality, what happens is that, as explained above, this adjective comes from the noun *division* and not directly from the verb *divide*. Therefore, this form is incorrect and its use should be avoided in any circumstance. It’s also not correct *divisible*, with C, avoid this form too.

### formal definition

Divisibility encompasses a series of rules that work as a mechanism to check if an integer *a* is divisible by another integer *b*.

We say that *b* divides *a* if it existsk∈Zsuch thatb×k=a. In such a case, we writeb|aand we call *b divisor of a*, and *a multiple of b*.

Another way of looking at it is through the Remainder Theorem, which tells us that: givena,b∈Zthere is only one pairk,r∈Zwith0≤r<bsuch thata=b×k+r, where *k* is called the quotient and *r* is the remainder. This implies that *b|a* if and only if the remainder of dividing *a* by *b* is *zero*.

### Rules and examples of divisibility

There are rules that allow us to immediately identify if a number is divisible by another and therefore it is convenient to keep in mind.

– Even numbers: A natural number is divisible by *2* if and only if it ends in *0, 2, 4, 6 or 8*.

– A number is divisible by *3* if and only if the sum of its digits is divisible by *3* . (Note that this rule can be applied recursively. That is if we want to check the divisibility of *613782*, we see that *6+1+3+7+8+2 = 27*, and *2+7 = 9*, and since *9* is divisible by *3*, so is *27* and so is *613782* .)

– A number is divisible by 4 if:

A) The number formed by the last two digits is divisible by *4*.

B) Ends at *00*.

C) Multiplying the last digit by *2* and adding the last digit we obtain a multiple of *4*.

– A number is divisible by *5* if it ends in *0* or *5*.

– A number is divisible by *9* if the sum of its digits is a multiple of *9*.

– A number is divisible by *11* if the sum of its digits in odd positions (counting from the right) minus the sum of its digits in odd positions is zero or a multiple of *11*.

The list goes on, but at some point, we should stop and establish criteria that allow us to combine these rules to deduce new ones, which is much more practical and possible than memorizing an infinite list.

Now you know the correct form of this term and that both ** divisible **and

**are written with S.**

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