What is a factor? What is a multiple?

An integer can be divisible by another integer, which is a factor of the former.

Example: 6 ÷ 2 = 3 2 and 3 are factors of 6.

An integer can be divisible by another integer, which is a multiple of another integer. For example, 15 can be divisible by 3 or 5, so 15 is a multiple of 3 and 5.

If a*b=c(a, B and C are all integers), then we call A and B factors of C. It should be noted that this relationship only holds when the dividend, divisor and quotient are integers and the remainder is zero. On the contrary, we call c a multiple of a and b, and we don't consider 0 when studying factors and multiples.

common factor

Definition: The common factor of two or more integers is called their common factor.

The greatest common factor of two or more integers is called their greatest common factor.

Inference: 1 is the common factor of any number of integers.

Between two nonzero natural numbers with multiple relationships, the smaller number is the greatest common factor of these two numbers.

Supplement:

1 divisibility: If the integer A is divisible by the non-zero integer B, the quotient is an integer and the remainder is zero, we say that A is divisible by B (or B is divisible by A) and record it as B | A. ..

2 prime number (prime number): a natural number with exactly two positive factors. (or defined as a number that is not divisible by other natural numbers except 1 and the integer itself among natural numbers greater than 1).

3 Composite number: There are other positive factors besides 1 and itself.

4 1 has only a positive factor of 1, so it is neither a prime number nor a composite number.

If A is a factor of B and A is a prime number, then A is a prime factor of B ... For example, 2, 3 and 5 are all prime factors of 30. 6 is not a prime number, so it doesn't count. 7 is not a factor of 30, so it is not a prime factor.

6 Two nonzero natural numbers whose common factor is only 1 are called prime numbers.

The number of positive factors of 7 1 nonzero natural number is limited, of which the smallest is 1 and the largest is itself. The multiples of nonzero natural numbers are infinite.

8 All nonzero integers are factors of 0. (still controversial)

9 2 is the smallest prime number.

10 4 is the smallest composite number.