1, divisible: If an integer A is divided by a natural number B to get an integer quotient C, and there is no remainder, it is said that A is divisible by B or B is divisible by A, and it is recorded as B/A. ..

2. Common symbols: the symbol "/"is separable, but the symbol ""cannot be separated; Because of the symbol "⊙", the symbol "∴";

Second, the separable judgment method:

1. is divisible by 2 and 5: the last digit is divisible by 2 and 5.

2. Divisible by 4 and 25: The number composed of the last two digits is divisible by 4 and 25.

3. It is divisible by 8. 125: The number composed of the last three digits is divisible by 8. 125.

4. Divisible by 3 and 9: The sum of the numbers on each digit is divisible by 3 and 9.

5. divisible by 7:

(1) The difference between the digits in the last three digits and the digits before the last three digits can be divisible by 7.

(2) Remove the last digit one by one and subtract twice the last digit to be divisible by 7.

6. divisible by 1 1:

The difference between the last three digits of (1) and the first three digits can be divisible by 1 1.

② The difference between the sum of numbers in odd digits and the sum of numbers in even digits can be divisible by 1 1.

③ Remove the last digit one by one, and the last digit can be divisible by 1 1.

7. Divisible by 13:

(1) The difference between the number composed of the last three digits and the number composed of the digits before the last three digits can be divisible by 13.

② Remove the last digit one by one. After subtracting 9 times of the last digit, it can be divisible by 13.

Third, the nature of separability:

1. If A and B are divisible by C, then (a+b) and (a-b) can also be divisible by C. ..

2. If A is divisible by B and C is an integer, then A multiplied by C can also be divisible by B. ..

3. If A can be divisible by B and B and C, then A can also be divisible by C. ..

4. If A is divisible by B and C, then A is divisible by the least common multiple of B and C. ..