Divisibility Criteria Explained

Divisibility Criteria Explained

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 that operation is a new integer. Or, put another way: if there is an integer C that multiplied by B gives A, then A is divisible by B.

For example : 8 is divisible by 4 since the result of the division is 2. Also, if we multiply 2 by 4, we will get 8 as a result.

With these ideas clear, we can turn to the notion of divisibility criteria. This is the name given to the rules that allow knowing if a number is divisible by another without the need to perform the operation in question.

  • Abbreviationfinder: Find definitions of English word – Hardware. Commonly used abbreviations related to word are also included.

The 5 divisibility criterion, to cite one case, states 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 9 divisibility criterion, on the other hand, indicates that numbers whose digits add up to a multiple of 9, are divisible by 9. Let’s see a case:

5949 is a number made up of the numbers 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 mentioned criterion of divisibility, we can affirm that 5949 is divisible by 9.

It is important to understand that knowledge of divisibility criteria can be very useful for people who work in certain branches of mathematics, or in other sciences in which the use of numbers at high levels of complexity is essential. For example, they are used to determine if a number is composite or prime, and also to decompose numbers into prime factors.

Having understood all this, we can move on to evaluating another of the many divisibility criteria that have been determined by mathematicians:

* 2 : it is the simplest of all, largely because it is the one we use on a daily basis 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 certain confusions can arise if we use a similar approach to that used in the previous criterion, since if we look only at the last number, expecting it to be odd, we will miss many numbers divisible by 3. The trick here it 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 divisible 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 on the far right, multiply it by 2 and then subtract the result from the number formed by the other figures; the process must be repeated until it is not 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 be 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.