How to decompose the prime factor of a number, how to decompose a number into prime factors.

As a simple example, the decomposed prime factors of 12 can be as follows: 12 = 2x2x3 = 4x3 = 1x12 = 2x6, where 1, 2, 3, 4, 6, and 12 can be said to be the factors of 12, that is, the multiplication of several numbers is equal to a natural number, then these numbers are the factors of this natural number. In 2, 3, 4, 2 and 3 are prime numbers, which are prime factors, and 4 is not prime numbers.

So what are prime numbers? That is, it can no longer be divided into numbers other than 1 and its own factors, such as 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, etc., there is no specific law for prime numbers, and there is no maximum prime number.

To find a number to decompose a prime factor, divide by the smallest prime number and divide until the result is prime. The formula for decomposing prime factors is called short division, which is similar to the nature of division, and can also be used to find the common factors of multiple numbers

Such as 242 24 (which is the symbol for short division).

3 – 3 is the prime number, the end.

It is obtained that 24 = 2 2 2 3 = 2 3 3 (m n = n power of m) and then 105---7 - 7 is a prime number, end.

Gives 105 = 3 5 7

1. Break this number into prime factors.

2. Add the power of each prime factor by 1, and then multiply the obtained sum.

For example: 12 = 2 to the 2nd power * 3 to the 1st power.

The number of factors of 12: (2+1)*(1+1)=6Validation: The factors of 12 are: 1,12,2,6,3,4.

There are two ways to decompose prime factors:

1. Multiplication.

It is written in the form of multiplying several prime numbers (these non-repeating prime numbers are prime factors), and the actual operation can be decomposed step by step.

For example, 36 = 2 * 2 * 3 * 3 can be gradually 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 prime. The equation for factoring prime factors is called short division.

Here's how to break it down:

The prime factor of 78 can be found by short division: 78 = 2 3 13.

The method of decomposing the prime factor is to remove the composite number with the smallest prime factor of a composite number, and if the resulting number is a prime number, it is written as the multiplication form of the composite number; If it is a composite number, it continues in the same way until it is finally a prime number.

There are two ways to decompose prime factors, and in addition to the most commonly used "short division decomposition method", there is also a "tower decomposition method".

Decomposing prime factors is of great help to solve some problems of natural numbers and products, and at the same time makes an important preparation for finding the greatest common divisor and least common multiples.

Step 1 4

Short division is to divide a divisor by a prime number that can be divisible by it, and so on, until the quotient is prime.

Step 2 4 Write the divisor sign, the integer to be decomposed is the dividend, and use the smallest prime number that can be divisible as the divisor.

Step 3 4 If the quotient is a composite number, divide it by the above method until the quotient is prime.

Step 4 4 Write the divisor and the final quotient in the form of multiplication, and complete the decomposition of the prime factor.

1. Break this number into prime factors.

2. Add the power of each prime factor by 1, and then multiply the obtained sum.

For example: 12 = 2 to the 2nd power * 3 to the 1st power.

The number of factors of 12: (2+1)*(1+1)=6Validation: The factors of 12 are: 1,12,2,6,3,4.

With short division. First of all, we must know the most basic: a single digit of 0 or 5 is divisible by 5; Even numbers are divisible by 2, add the digits of each bit, add them up if the result is not a single digit until they end up in a single digit, and if the single digit is divisible by 3, then the number is divisible by 3.

After getting a number, first use the above principles to remove all the factors (that is, until you know that it is not divisible), and then decompose the remaining relatively large factors depends on experience

Tip: The number of prime numbers with a single digit is the most (e.g. , etc.), and only a multiple of the prime number with a single digit is possibleThe single digit is a multiple of the prime numbers of 3 and 7, and the single digit can appear 9

Generally, it is impossible to come up with numbers that are difficult to decompose, so it may seem complicated to say, but the process is actually very simple.