Many people remember from the school curriculum that there are signs of divisibility. By this phrase is understood the rules that allow you to quickly determine whether a number is a multiple of a given without performing a direct arithmetic operation. This method is based on actions performed with part of the digits from a record in a positional number system.
The simplest signs of divisibility are remembered by many from the school curriculum. For example, the fact that all numbers are divisible by 2, the last digit in the record of which is even. This feature is most easily remembered and put into practice. If we talk about the method of dividing by 3, then for multi-valued numbers the following rule applies, which can be shown by such an example. You need to find out if there will be 273 times three. To do this, perform the following operation: 2 + 7 + 3 = 12. The resulting amount is divided by 3, therefore, 273 will be divided by 3 in such a way that the result is an integer.
Signs of divisibility by 5 and 10 will be as follows. In the first case, the record will end with the numbers 5 or 0, in the second case only with 0. In order to find out if the number divisible by four is divisible by one, do the following. It is necessary to isolate the last two digits. If it is two zeros or a number that is divisible by 4 without a remainder, then all the dividends will be a multiple of the divisor. It should be noted that the listed signs are used only in the decimal system. They are not used in other numeration methods. In such cases, their own rules are derived, which depend on the basis of the system.
The signs of dividing by 6 are as follows. A number is a multiple of 6 if it is a multiple of both 2 and 3. In order to determine whether a number is divisible by 7, you need to double the last digit in its entry. 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. You need to find out if the number 364 is a multiple of seven. For this, 4 is multiplied by 2, it turns out 8. Next, the following action is performed: 36-8 = 28. The result obtained is a multiple of 7, and, therefore, the initial number 364 can be divided by 7.
Signs of divisibility by 8 are as follows. If the last three digits in the record of a number form a number that is a multiple of eight, then the number itself will be divided by a given divisor.
To find out if a multiple-digit number is divisible by 12, see the following. From the signs of divisibility listed above, it is necessary to find out whether the number 3 and 4 is a multiple. If they can simultaneously act as divisors for a number, then with the given dividend, you can also perform the division by 12. A similar rule applies to other complex numbers, for example, fifteen. In this case, the divisors should be 5 and 3. To find out if the number is divisible by 14, you should see if it is a multiple of 7 and 2. So, you can consider this with 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 you need to subtract 16. The result of 49 is divided by 7, like the whole number. Therefore, 658 can be divided into 14.
If the last two digits in a given number are divided by 25, then all of it will be a multiple of this divisor. For multi-digit numbers, the sign of divisibility by 11 will sound as follows. You need to find out if the given divisor is a multiple of the difference in the sums of digits that are on odd and even places in his record.
It should be noted that the signs of divisibility of numbers and their knowledge very often greatly simplifies many tasks that are encountered not only in mathematics, but also in everyday life. Thanks to the ability to determine whether a number is a multiple of another, various tasks can be quickly completed. In addition, the use of these methods in mathematics will help to develop logical thinking in students or schoolchildren, and will contribute to the development of certain abilities.