Factors: Determining factors by tree and factorization method

 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: 2⁵x7.

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 3¹x13¹.

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 3³x7.

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 5¹x23¹

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.