"Integer and divisibility" is the knowledge point of the fourth grade primary school of Mathematics People's Education Press. The main contents are as follows:

1, meaning of integer: both natural numbers and 0 are integers.

2. Natural number: 1, 2, 3, which is called natural number when we count objects. There is no object, which is represented by 0. 0 is also a natural number.

3. Counting units: one (one), ten, one hundred, one thousand, ten thousand, one hundred thousand, one million, ten million and one hundred million are all counting units. The propulsion rate between every two adjacent counting units is 10. This counting method is called decimal counting method.

4. Digits: Counting units are arranged in a certain order, and their positions are called digits.

5. Divisible number:

Integer a divided by integer b (bne; 0), the quotient of division is an integer without remainder, so we say that A is divisible by B, or that B is divisible by A. ..

If the number A is divisible by the number B (b ne0), A is called a multiple of B, and B is called a divisor of A (or a factor of A). Multiplication and divisor are interdependent.

Characteristics of separability:

1. If the last digit of a number is an even number, the number can be divisible by 2.

2. If the sum of all digits of a number is divisible by 3, then this integer can be divisible by 3.

3. If the last two digits of a number are divisible by 4, then the number can be divisible by 4.

If the last digit of a number is 0 or 5, the number can be divisible by 5.

If a number is divisible by 2 and 3, it can be divisible by 6.

6. If one digit of a number is truncated, subtract twice the number from the remaining number. If the difference is a multiple of 7, the original number can be divisible by 7.

7. If the last three digits of a number are divisible by 8, then the number can be divisible by 8.

8. If the sum of all digits of a number is divisible by 9, then the integer can be divisible by 9.

9. If the last digit of a number is 0, it can be divisible by 10.

10. If the difference between the sum of odd digits and the sum of even digits of a number is divisible by 1 1, then the number can be divisible by 1 1. The multiple test method of 1 1 can also be treated by the "tail-cutting method" of the above-mentioned inspection 7. The only difference in the process is that the multiple is 1 instead of 2.

1 1. If a number is divisible by 3 and 4, it can be divisible by 12.

12. If the single digits of a number are truncated and then four times the single digits are added to the remainder, if the sum is a multiple of 13, the original number can be divisible by 13.

13. If one digit of a number is truncated, subtract 5 times of this number from the remaining number. If the difference is a multiple of 17, the original number can be divisible by 17. If the difference is too big or it is not easy to see whether it is a multiple of 17 in mental arithmetic, repeat the previous process until it can be clearly judged.

14. If the single digit of a number is truncated, then twice the single digit is added to the remaining numbers. If the difference is a multiple of 19, the original number can be divisible by 19. If the difference in mental arithmetic is too big or it is not easy to see whether it is a multiple of 19, repeat the previous calculation ideas until you can clearly judge.

15. If the difference between the last three digits of a number and the three times of the previous separated number can be divisible by 17, then this number can be divisible by 17.

16. If the difference between the last three digits of a number and the preceding seven-separated number is divisible by 19, then the number can be divisible by 19.

17. If the difference between the last four digits of a number and the first five times of the separated number can be divisible by 23 (or 29), then the number can be divisible by 23.

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