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Common methods of decomposing prime factors in junior high school mathematics
Many students will encounter the problem of factorization when they study mathematics. I sorted out some methods to decompose prime factors. Let's have a look.

Decomposition factor method 1, multiplication

It is written by multiplying several prime numbers (these non-repeated prime numbers are prime factors), and the actual operation can adopt the method of gradual decomposition.

For example, 36=2*2*3*3 can be decomposed into 36=4*9=2*2*3*3 or 3* 12=3*2*2*3.

2. Short division

Divide from the smallest prime number until the result is a prime number. The formula for decomposing prime factors is called short division.

Proof that there is no maximum prime number in factorization prime factor theorem: (by reduction to absurdity)

Suppose that the largest prime number is n, and all prime number sequences are: N 1, N2, n3 ... n ... noun (abbreviation of noun).

Let m = (n/kloc-0 /× N2× n3× n4× ... n)+1,

It can be proved that m is not divisible by any prime number, and it is concluded that m is also a prime number.

And M>n contradict the hypothesis, so it can be proved that there is no maximum prime number.

Prime factor knowledge decomposition 1, factor and multiple: in integer multiplication, if a× b = c, then a and b are factors of c, and c is a multiple of a and b.

For convenience, when studying factors and multiples, the numbers we refer to are all integers (generally excluding 0). But 0 is also an integer.

3. The minimum factor of a number is 1, and the maximum factor is itself. The number of factors of a number is limited.

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

If both integers (a, b) are multiples of another integer (c), then the sum of these two integers (a+b) is also a multiple of another integer (c).

5. Numbers with 0, 2, 4, 6 and 8 are multiples of 2.

Numbers with 0 and 5 are multiples of 5.

A numb with a unit of 0 is a multiple of both 2 and 5.

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

The above is some information about prime factor decomposition, hoping to help everyone.