Signs of the divisibility of numbers

From the school program, many remember that there are signs of divisibility. Under this phrase are understood rules that allow you to quickly determine whether a number is a multiple of a given number without performing a direct arithmetic operation. This method is based on the actions performed with a part of the digits from the record in the positional number system.

The most simple signs of divisibility, many remember from the school program. For example, the fact that on 2 divide all the numbers, the last digit in the records of which is even. This feature is most easily remembered and applied in practice. If we talk about the method of division by 3, then for many-valued numbers the following rule applies, which can be shown in this example. It is necessary to find out whether 273 is a multiple of three. To do this, perform the following operation: 2 + 7 + 3 = 12. The resulting sum is divided by 3, and therefore 273 will be divided into 3 in such a way that the result is an integer.

The signs of divisibility by 5 and 10 will be as follows. In the first case, the record will end in numbers 5 or 0, in the second case only 0. To find out whether the dividend is divisible by four, proceed as follows. It is necessary to isolate the last two digits. If there are two zeros or a number that is divisible by 4 without a remainder, then the entire dividend will also be a multiple of the divisor. It should be noted that the listed characteristics are used only in the decimal system. They are not used in other ways of calculating. In such cases, their rules are derived, which depend on the basis of the system.

Signs of division into 6 are as follows. The number is a multiple of 6 if it is a multiple of both 2 and 3. In order to determine if the number is divided by 7, you need to double the last digit in its record. The result is subtracted from the original number, which does not take into account the last digit. This rule can be considered in the following example. It is necessary to know whether the seven is a multiple of 364. For this, 4 is multiplied by 2, it turns out 8. Then the following action is performed: 36-8 = 28. The result is a multiple of 7, and, consequently, the original number 364 can be divided by 7.

The signs of divisibility by 8 are as follows. If the last three digits in the number record form a number that is a multiple of eight, then the number itself will be divisible by a given divisor.

To find out whether a multivalued number is divisible by 12, we can proceed as follows. According to the divisibility criteria listed above, it is necessary to find out if the numbers 3 and 4 are divisible. If they can act simultaneously as divisors for a number, then the divide operation can be carried out with a given divisible by 12. A similar rule applies to other complex numbers, for example, fifteen. In this case, divisors should be 5 and 3. To see if the number is divided by 14, you should see if it is a multiple of 7 and 2. So, you can see this in the following example. It is necessary to determine whether 658 can be divided by 14. The last digit in the record is even, therefore, the number is a multiple of two. Next, we multiply 8 by 2, we get 16. From 65, we subtract 16. Result 49 is divided by 7, like the whole number. Therefore, 658 can be divided into 14.

If the last two digits in the given number are divided by 25, then all of it will be a multiple of this divisor. For many-valued numbers, the divisibility criterion on 11 will be as follows. It is necessary to find out whether the difference in the sums of digits that stand on odd and even places in its record is multiples of the given divisor.

It should be noted that the signs of divisibility of numbers and their knowledge very often greatly simplifies many problems that occur not only in mathematics, but also in everyday life. Due to the ability to determine if a number is a multiple of one, you can quickly perform various tasks. In addition, the use of these methods in math classes will help develop logical thinking among students or schoolchildren, will contribute to the development of certain abilities.