Indications of divisibility

The rules for dividing by numbers from 1 to 10, as well as on11 and 25 were derived to simplify the process of dividing the natural numbers. Those of them that end in 2, 4, 6, 8, 0 are considered even.

What are the signs of divisibility?

In fact, this is an algorithm that allows you to quicklyDetermine whether the number is divisible by the one given in advance. In the case when the divisibility criterion makes it possible to clarify the remainder of the division, it is called a sign of equicontinuity.

Sign of divisibility by 2

The number can be divided into two if the last digit is even or zero. In other cases, it will not be possible to divide.

For example:

52 734 is divided by 2, because its last digit is 4 - that is, even. 7 693 is not divisible by 2, since 3 is odd. 1 240 is divided, because the last digit is zero.

Symptoms of divisibility by 3

The number 3 is multiples of only those numbers for which the sum is divided by 3

Example:

17 814 can be divided into the figure 3, because the total sum of its digits is 21 and divided by 3.

Sign of divisibility by 4

The number can be divided by 4 if the last two digits of the zero are zero or can form a multiple of 4. In all other cases, it will not be possible to divide.

Examples:

31 800 can be divided into 4, because at the endit's two zeros. 4 846 854 is not divisible by 4 because the last two digits form the number 54, and it is not divisible by 4. 16 604 is subdivided by 4, because the last two digits 04 form the number 4, which is divided by 4.

Sign of divisibility by 5

5 times the number, in which the last digit is zero or five. All others - do not share.

Example:

245 is a multiple of 5, because the last digit of 5.774 is not a multiple of 5 because the last digit is four.

Indication of divisibility by 6

The number can be divided by 6, if it can be simultaneously divided into 2 and 3. In all other cases - not divided.

For example:

216 can be divided into 6, because it is a multiple of two and three.

Sign of divisibility by 7

Multiply the 7th number in the event that when subtracting the last doubled digit from this number, but without it (without the last digit), a value that can be divided by 7 is obtained.

For example, 637 is a multiple of 7, because 63- (2 · 7) = 63-14 = 49. 49 can be divided into.

Sign of divisibility by 8

Looks like a sign of divisibility by 4. The number can be divided by 8 if three (and not two, as in the case of the four) last zeros or can form a number that is a multiple of 8. In all other cases, it is not divisible.

Examples:

456 000 can be divided into 8, because at the endit has three zeros. 160 003 will not be divided by 8, because the last three digits form the number 4, which is not a multiple of 8. 111 640 multiples of 8, because the last three digits form the number 640, which can be divided into 8.

For information: you can call the same signs for dividing by numbers 16, 32, 64 and so on. But in practice they do not matter.

The divisibility of 9

9-xe are multiples of those numbers whose sum of digits can be divided by 9.

For example:

The number 111 499 by 9 is not divisible, because the sum of the digits (25) by 9 is not divided. The number 51 633 can be divided by 9, because its sum of digits (18) is 9-fold multiple.

Signs of divisibility by 10, per 100 and 1000

On 10, you can divide those numbers, the last digit of which is 0, on 100-t, for which the last two digits are zeros, by 1000 - those with the last three digits of zero.

Examples:

4500 can be divided into 10 and 100. 778,000 multiples and 10, and 100, and 1000.

Now you know which features of the divisibility of numbers exist. Successful calculations to you and do not forget about the main thing: all these rules are given for simplification of mathematical calculations.

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