1, A× B = C (A, b and c are integers not equal to 0), c is a multiple of a and b, and a and b are factors of c. ..

How to find the factor:

The number of factors of a number is limited, in which the smallest factor is 1 and the largest factor is itself.

The number of multiples of a number is infinite, and the smallest multiple is itself.

2. Natural numbers are divided according to whether they are multiples of 2: odd and even.

Odd number: not a multiple of 2.

Even number: It is a multiple of 2 (0 is also an even number).

The smallest odd number is 1 and the smallest even number is 0.

Numbers in units of 0, 2, 4, 6 and 8 are all multiples of 2.

A number with 0 or 5 is a multiple of 5.

The sum of the numbers on each digit of a number is a multiple of 3, and this number is a multiple of 3.

The largest two digits that can be multiples of 2, 3 and 5 are 90, and the smallest three digits are 120.

3. Natural number divided by the number of factors: prime number, composite number, 1.

Prime number: There are only two factors, 1 and itself.

Composite number: There are at least three factors, 1, itself and other factors.

1: There are only 1 factors. 1' is neither a prime number nor a composite number.

The smallest prime number is 2 and the smallest composite number is 4.

Prime numbers within 20: 8 (2, 3, 5, 7, 1 1 3, 17, 19).

Prime numbers within 100: 2, 3, 5, 7,1,13, 17, 19, 23, 29, 3/kloc-0.

43、47、53、59、6 1、67、7 1、73、79、83、89、97

4. Prime factorization

Decomposition of prime factors by short division (a composite number is written in the form of multiplication of several prime numbers)

5, common factor, the greatest common factor

The common factor of several numbers is called the common factor of these numbers. The largest of them is called their greatest common factor.

Find the greatest common factor of two or three numbers by short division (multiply all the divisors until they are coprime)

The common factor of several numbers is only 1, so they are coprime.

Special case of coprime of two numbers;

(1) 1 is coprime with any natural number; (2) Two adjacent natural numbers are coprime; (3) Two prime numbers must be coprime;

(4) 2 and all odd coprime; 5] prime number is coprime with a composite number smaller than it;

6, common multiple, minimum common multiple

The common multiple of several numbers is called the common multiple of these numbers. The smallest one is called their least common multiple.

Find the least common multiple of two numbers by short division (multiply all divisors and quotients until they are coprime)

Find the least common multiple of three numbers by short division (multiply all divisors and quotients until they are pairwise coprime)

If two numbers are multiples, then the smaller number is their greatest common factor;

Larger numbers are their least common multiple.

If two numbers are coprime, then 1 is their greatest common factor.

Their product is their least common multiple.