Question

prime factorization method ​

Answer 1

Answer:

A prime number can only be divided by 1 or itself, so it cannot be factored any further! Every other whole number can be broken down into prime number factors. It is like the Prime Numbers are the basic building blocks of all numbers.

Answer 2

Answer:

Prime Factorization Methods

The most commonly used prime factorization methods are:

Division Method

Factor Tree Method

Division Method

The steps to calculate the prime factors of a number is similar to the process of finding the factors of a large number. Follow the below steps to find the prime factors of a number using the division method:

Step 1: Divide the given number by the smallest prime number. In this case, the smallest prime number should divide the number exactly.

Step 2: Again, divide the quotient by the smallest prime number.

Step 3: Repeat the process, until the quotient becomes 1.

Step 4: Finally, multiply all the prime factors

Example:

Below is a detailed step-by-step process of prime factorization by taking 460 as an example.

Step 1: Divide 460 by the least prime number i.e. 2.

So, 460 ÷ 2 = 230

Step 2: Again Divide 230 with the least prime number (which is again 2).

Now, 160 ÷ 2 = 115

Step 3: Divide again with the least prime number which will be 5.

So, 115 ÷ 5 = 23

Step 4: As 23 is a prime number, divide it with itself to get 1.

Now, the prime factors of 460 will be 22 x 5 x 23

Factor Tree Method

To find the prime factorization of the given number using factor tree method, follow the below steps:

Step 1: Consider the given number as the root of the tree

Step 2: Write down the pair of factors as the branches of a tree

Step 3: Again factorize the composite factors, and write down the factors pairs as the branches

Step 4: Repeat the step, until to find the prime factors of all the composite factors

In factor tree, the factors of a number are found and then those numbers are further factorized until we reach the closure. Suppose we have to find the factors of 60 and 282 using a factor tree. Then see the diagram given below to understand the concept.

Factor tree

In the above figure, we can number 60 is first factorized into two numbers i.e. 6 and 10. Again, 6 and 10 is factorized to get the prime factors of 6 and 10, such that;

6 = 2 x 3

and 10 = 2 x 5

If we write the prime factors of 60 altogether, then;

60 = 6 x 10 = 2 x 3 x 2 x 5

Same is the case for number 282, such as;

282 = 2 x 141 = 2 x 3 x 47

So in both cases, a tree structure is formed.