What is Divisibility criteria?

What Does Divisibility criteria Mean

A criterion is a norm, an opinion or a judgment. Divisibility , on the other hand, is the characteristic of what can be divided (split, separate or split).

An integer A is said to be divisible by another integer B when the result of this operation is a new integer. Or, in other words: whether there is a whole number C which, multiplied by B , resulting A , A is divisible by B .
For example : 8 is divisible by 4 since the result of division is 2 . Also, if we multiply 2 by 4 , we will get 8 as a result.

With these ideas clear, we can focus on the notion of divisibility criteria . This is the name of the rules that allow us to know if a number is divisible by another without the need to perform the operation in question.
The divisibility criterion of 5 , to cite one case, indicates that a number is divisible by 5 when its last digit is a 5 or a 0 . In this way, we know that the numbers 15 , 65 , 70 , 150 , 365 , 2630 and 80595 , among many others, are divisible by 5 .
The divisibility criterion of 9 , on the other hand, indicates that the numbers whose numbers added together give a multiple of 9 are divisible by 9 . Let's look at a case:
5949 is a number made up of the digits 5 , 9 , 4 and 9 . If we add these values ( 5 + 9 + 4 + 9 ), we will get 27 as a result. 27 , in turn, is a multiple of 9 since 9 x 3 = 27 . Taking into account the aforementioned divisibility criterion, we can affirm that 5949 is divisible by 9 .
It is important to understand that knowledge of the divisibility criteria can be very useful for people who are dedicated to certain branches of mathematics, or to other sciences in which the use of numbers at high levels of complexity is essential. For example, they are used to determine whether a number is composite or prime , and also to decompose numbers into prime factors.
Having understood all this, we can proceed to evaluate other of the many divisibility criteria that have been determined by mathematicians:
* 2 : it is the simplest of all, in large part because it is the one we use every day even outside the field of mathematics . Basically, a number is divisible by 2 if its last digit is even, that is, if it is 0, 2, 4, 6 or 8 ;

* 3 : in this case there may be some confusion if we use an optics similar to that used in the previous criterion, since if we look only at the last figure, expecting it to be odd, we will ignore many numbers divisible by 3. The trick here is to add all the figures and check if the result is a multiple of 3. For this reason, the number 480 passes the test, since 4 + 8 + 0 = 12 ;
* 4 : the divisibility criterion of 4 establishes that the last two digits of a number divisible by it must be one of its multiples , two zeros in a row, or that their sum must result in one of its multiples. For example, 112, 2300, and 928 are divisible by 4, since 12 is a multiple of 4, 2300 ends in 00, and 2 * 8 = 16 (a multiple of 4);
* 6 : to know if a given number is divisible by 6, it must be so by 2 and 3 at the same time, so we must know their respective divisibility criteria;
* 7 : this criterion is somewhat more complicated to apply than the previous ones, since we must isolate the figure that is in the extreme right, multiply it by 2 and then subtract the result from the number formed by the other figures; the process should be repeated until it is no longer possible to continue. If the final result is 7 or 0, then the original number is divisible by 7;
* 8 : to know if a number is divisible by 8, its last three digits must be one of its multiples or three zeros;
* 10 : of all the divisibility criteria exposed so far, this is the one with the fewest rules , since any number ending in 0 is divisible by 10.

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