A common factor is a factor that exists in two or more numbers.

For example, the common factor of 10 and 5 is 1 5.

Because the common factor of 10 is 1, 2,5, 10.

The common factor of 5 is 1, 5. So the common factor of 10 and 5 is 1 5.

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The common multiples of two numbers a and b are both multiples of a and b, that is, they can be divisible by a and b at the same time.

For example: 12 and 15, their common multiples are 60, 120, 180 and so on.

The smallest of these common multiples is called the least common multiple, which is 60.

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The concept of prime number

If a number has only two factors: 1 and itself, it is called a prime number. For example, (within 10) 2, 3, 5 and 7 are prime numbers, and 4, 6, 8 and 9 are not. The latter is called a composite number or a composite number. Specifically, 1 is neither a prime number nor a composite number. From this point of view, integers can be divided into two types, one is called prime number and the other is called composite number. (1 is neither a prime number nor a composite number) The famous Gauss "unique decomposition theorem" says that any integer. It can be written as the product of a series of prime numbers. All prime numbers are odd except that 2 is even.

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The concept of composite number

Besides 1 and itself, there are other factors. A composite number has at least three factors.

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1 is neither prime nor composite. 1 has only one divisor of its own, and 0 has countless divisors (except itself), so it is more reasonable to divide natural numbers into "prime number, composite number, 0, 1".

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Characteristics of factors of a number:

(1) The maximum factor is itself, and the minimum factor is 1.

(2) The number of factors is limited.

Characteristics of multiples of a number:

(1) The minimum multiple is itself, and there is no maximum multiple.

(2) The number of multiples is infinite.