**Determining factors**
is one of the important parts of factorization. We see a different question
related to determining factors of numbers and algebraic expressions. Today we
learn to **find
factors** of different numbers step by step.

# What is a factor tree?

The
prime factorization of a number may be represented through the use of the **factor tree**
method. It is a way to represent the components that comprise a number in the
form of a tree. A picture is given below.

**How do you determine the factor tree for 72?**

We
use the tree method to **determine the factor tree for 72**. since 72 is a
composite number. The factors of 72 are 1,2,3,4,6,8,9,12,18,24,36,72.
We can represent a **factor tree of 72 **in the following form.

# Determine the factors of 224:

224
is a composite number and we can find its prime factors by the following
method. The prime factors of 224 can be written as 2x2x2x2x2x7, and we write
the prime **factors
of 224 in index notation:** 2^{5}x7.

# What are the factors of 39?

39
also comes in the category of composite numbers. Its prime factor will be 3x13.
The index notation of the factors of 39 will be 3^{1}x13^{1}.

**What are the factors of 97?**

97
can only be a factor of 1 because it is a prime number, and we can find the** factors
of 97** in the following way.

# Index notation for 189 factors:

189
is a multiple of 3, 7, 9,21, 27, and 63, and its prime will be 3x3x3x7. The **factors of
189 in index notation** will be presented in writing as 3^{3}x7.

# Index notation of the prime factors of 115:

115
is a multiple of 5, 23, and if we can write the **prime factors of 115** in index
notation, we will be 5^{1}x23^{1}

^{}

**Tree factors for 500:**

500
is a multiple of various numbers. The **tree factor for 500** will be presented in
the writing form:

# How can we find the factors of -8x-32 in an easy way?

We find the **factor of -8x-32 in an easy way**. -8 is a common factor in the given
algebraic expression i.e., -8x-32, so -8 will be its common factor, and we will
find its solution as given below.

Q: -8𝑥-32

Sol:

-8(1𝑥+4) **Ans**

So,
we learn how to **determine prime factors
by the factorization method and tree method** of different numbers.

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