# How do you make a prime factorization tree?

As detailed below.

Prime factorization is the method of representing a number in the form of its prime factors. Just to recall that prime numbers are the numbers that are divisible only by 1 and itself.

Prime factors are the prime numbers by which the given number is divisible. When the prime factors of a number are multiplied, we obtain the given number.

The tree method of prime factorization is very simple and quite useful in order to calculate lowest common multiple (LCM) and highest common factor (HCF).

The factors in this method may be obtained using different combinations but the prime factors of a number will always be unique.

In prime factorization tree method, we are supposed to follow the following steps:

Step 1 : Divide the given number in two factors.

Step 2 : Now divide these two factors into other two multiples.

Step 3 : Repeat the step 2 until we reach all prime factors.

Step 4 : All the prime factors so obtained collectively known as prime factors of given number. In order to cross check; multiply all the prime factors, you must get the given number.

We can illustrate prime factorization tree method through a simple example. Let’s draw the factor tree for number 48.

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To make a prime factorization tree, follow these steps:

- Start by writing the number you want to factorize at the top of the page.
- Identify the smallest prime number that can divide the given number evenly (without leaving a remainder). This is usually 2 for even numbers and 3 for odd numbers.
- Write this prime number on the next level down, and write the result of dividing the original number by this prime number below it.
- Continue dividing the numbers at each level by prime numbers until you reach a point where the number cannot be divided further.
- Repeat this process for each new number until all the branches end in prime numbers.

Example: Let's say we want to find the prime factorization of 36.

- Start with 36 at the top.
- The smallest prime number that can divide 36 evenly is 2. So, write 2 on the next level down and 36 ÷ 2 = 18 below it.
- The smallest prime number that can divide 18 evenly is also 2. So, write 2 on the next level down and 18 ÷ 2 = 9 below it.
- The smallest prime number that can divide 9 evenly is 3. So, write 3 on the next level down and 9 ÷ 3 = 3 below it.
- The smallest prime number that can divide 3 evenly is 3. So, write 3 on the next level down and 3 ÷ 3 = 1 below it.

The prime factorization of 36 is 2 × 2 × 3 × 3, or written in exponential form: (2^2 \times 3^2).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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