1. Factor definition
In primary school mathematics, two positive integers are multiplied, so both numbers are called factors of product, or divisors.
Definition of primary school mathematics: If a*b=c(a, B and C are all integers), then A and B are the 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. Conversely, C is called a multiple of A and B. When learning factors and multiples, primary school mathematics does not consider 0.
In fact, factors are generally defined as integers: let a be an integer and b be a non-zero integer. If there is an integer Q that makes A=QB, then B is a factor of A, denoted as B | A ... but some authors do not require B≠0. For example, 2X6= 12, and the product of 2 and 6 is 12, so 2 and 6 are factors of 12. 12 is a multiple of 2 and also a multiple of 6. 3X(-9)=-27, 3 and -9 are all factors of -27. -27 is a multiple of 3 and -9.
Generally speaking, the integer A is multiplied by the integer B to get the integer C. Both the integer A and the integer B are called factors of the integer C. Conversely, the integer C is a multiple of the integer A and also a multiple of the integer B. ..
2. Related nature
Divisibility: If the integer A is divisible by the non-zero integer B, the quotient is an integer, and the remainder is zero, it is said that A is divisible by B (or B is divisible by A), and it is recorded as B | A ... Prime number (prime number): a natural number with exactly two positive factors. (or defined as a number that cannot be divisible by other natural numbers except 1 and the integer itself among natural numbers greater than 1).
Composite number: There are other positive factors besides 1 and itself. 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. Two nonzero natural numbers whose common factor is only 1 are called coprime numbers. The number of positive factors of 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.