Signs of divisibility of numbers

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from the curriculum many remember that there are signs of divisibility.Under this phrase understand the rules that allows you to quickly determine whether a number is a multiple of the set, while not making an immediate arithmetic operation.This method is based on the actions performed with the part numbers of entries in the positional notation.

most simple signs of divisibility many remember from the curriculum.For example, the fact that all the numbers are divided into two, the last figure in the record that is even.This feature is most easily remember and apply in practice.If we talk about the process of dividing by 3, then the multi-digit numbers following rule applies, which can be shown by the following example.It is necessary to find out whether 273 is a multiple of three.To do this, do the following: 2 + 7 + 3 = 12.The resulting sum is divided by 3, therefore, 273 to be divided by 3, so that the result is an integer.

Divisibility by 5 and 10 are as follows.In the first case, the recording will end at the numbers 5 and 0 in the second case, only 0. In order to find out whether the dividend is a multiple of four, should be done as follows.It is necessary to isolate the last two digits.If the two zero or a number which is divisible by 4 without a remainder, all the dividend is a multiple of the divisor.It should be noted that these features are only used in the decimal system.They do not apply to other methods of calculation.In such cases, to withdraw their rules that depend on the base system.

Signs of division 6 following.Number 6 fold if it is a multiple 2, and 3. In order to determine whether the number is divisible by 7, to double last digit of its recording.The result is subtracted from the original number, which does not take into account the last digit.This rule can consider the following example.It is necessary to find out whether a multiple of seven the number 364. For this 4 multiplied by 2 turns 8. Then perform the following actions: 36-8 = 28.The result is a multiple of 7, and, therefore, the initial number of 364 can be divided into 7.

Divisibility by 8 read as follows.If the last three digits in record numbers form a number that is a multiple of eight, the number itself will be divided by a predetermined divisor.

find out whether the divided multi-valued number to 12, as follows.According to the above features divisibility need to know whether the number is a multiple of 3 and 4. If they can act at the same time for the number of divisors, then specify the dividend can be carried out and the operation of dividing by 12. This rule applies to other complex numbers, for example, fifteen.Thus dividers 5 have to act and 3. To determine whether a number is divided by 14, should see whether it is a multiple of 7, and 2. Thus, it can consider the following example.It is necessary to determine whether it is possible to divide 658 by 14. The last figure in the record is even, hence the number is a multiple of two.8 Next, we multiply by 2, we get 16. Of the 65, you subtract 49 16. The result is divided by 7, as well as all the numbers.Consequently, the 658 can be divided and 14.

If the last two digits of a given number divided by 25, then all it will be a multiple of this divisor.For multi-digit numbers divisible by 11 sign would read.It is necessary to find out whether a given multiple of the difference between the sum of digits of the divisor, which are on the odd and even field in its record.

should be noted that the signs of divisibility of numbers and their knowledge is often greatly simplifies many tasks, which are found not only in mathematics, but also in everyday life.Thanks to the ability to determine whether the number is a multiple of the other, you can quickly perform various tasks.In addition, the use of these methods in the classroom Mathematics helps develop logical thinking in students and pupils, will facilitate the development of certain abilities.