1. If the number A is divisible by the number B (b≠0), then A is called a multiple of B and B is called a factor of A. ..

2. When the integer A is divided by the integer b(b≠0), the quotient is exactly an integer with no remainder, so we say that A is divisible by B, or that B is divisible by A. 。

3. Because any integer can be divisible by 1, any integer is a multiple of 1, and 1 is a factor of any integer.

4. Because 0 can be divisible by any non-zero integer, 0 is a multiple of any non-zero integer, and any non-zero integer is also a factor of 0. For convenience, when we study factors and multiples, the numbers we refer to generally refer to natural numbers that are not zero. )

5. The smallest factor is 1, and the largest factor is itself; The number of factors of a number is infinite.

6. The minimum multiple of a number is itself, and there is no maximum multiple; The multiple of a number is infinite.

7. Numbers 0, 2, 4, 6 and 8 are divisible by 2. Numbers that are divisible by 2 are called even numbers, such as 2, 4, 6, 8, 10, 12 ... numbers that are not divisible by 2 are called odd numbers (j:), such as 65438+.

8. A number with a bit of 0 or 5 can be divisible by 5; The sum of the numbers in each digit of a number can be divisible by 3, and this number can also be divisible by 3.

9. If the last two digits of a number are divisible by 4, then this number can be divisible by 4; If the sum of digits of a number is divisible by 9, then the number can be divisible by 9.

10. If a number has only two factors, namely 1 and itself, then this number is called a prime number (also called a prime number).

1 1. If a number has other factors besides 1 and itself, it is called a composite number.

12. If the factor of a natural number is a prime number, this factor is called the prime factor of this natural number.

13. Each composite number can be written as the product of several prime factors; Multiplying a composite number by a prime factor is called prime factor decomposition.

14. When decomposing a prime factor by short division, first divide by a prime number (usually starting from the smallest number). If the quotient is a prime number, write the divisor and quotient as multiplication. If the quotient is a composite number, continue to divide by the above method until the quotient is a prime number. Then write each divisor and the final quotient in the form of multiplication.

15. The common factor of several numbers is called the common factor of these numbers; The largest one is called the greatest common factor of these numbers.

16. Two numbers whose common factor is only 1 are called prime numbers. If both numbers are prime numbers, then their greatest common factor is only 1.

17. If the smaller number is a factor of the larger number, then their greatest common factor is the smaller number.

18. Find the greatest common factor of two numbers by decomposing prime factors. Generally, it is divided by the prime factor shared by these two numbers until the quotient obtained is a prime number, and then all the divisors are multiplied.

19. The common multiple of several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers.

20. If two numbers are prime numbers, then their least common multiple is the product of these two numbers.

2 1. If a larger number is a multiple of a smaller number, then their least common multiple is this larger number.

22. Find the least common multiple of two numbers by decomposing prime factors. Generally, divide by the prime factor shared by these two numbers until the quotient is a prime number, and then multiply all the divisors by the last two quotients.