# Prime Factorization

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Prime Factorization is the process of expressing a given number as a product of prime factors.

Consider a number say 30. This is a composite number. We can write 30 as

30 = 2 x 15. But 15 is also composite number which can be written as

15 = 3 x 5

∴ 30 = 2 x 3 x 5

When we write 30 = 2 x 3 x 5, none of the numbers 2, 3, 5 are composite numbers.

2, 3, and 5 are prime factors of 30.

Thus we can say that 30 = 2 x 3 x 5 is the prime factorisation of 30.

There are two methods to find the factors of the given numbers.

1) Factor tree

2) Prime Factorisation Method

Factor tree

Example: Factor tree of 72 is given below.

Prime Factorisation Method

Another method to find the factors of the given number. Here also use the prime numbers. So start with 2 ,3,5,7 according to divisibility of the number. If we start with 2 then complete the division by 2 and then consider the next prime numbers.

Express the following as product of prime factors.

1) 150

150 = 2 x 75

= 2 x 3 x 25

= 2 x 3 x 5 x 5

The prime factors of 150 are 2 x 3 x 5 x 5

2) 732

732 = 2 x 366

= 2 x 2 x 183

= 2 x 2 x 3 x 61
_______________________________________________________________
Practice

Using prime numbers, find the factors of the following :
1) 1331
2) 164
3) 729
4) 180
5) 5000
6) 84
7) 91
8) 105
9) 1000
10) 48

Factors and Multiples

Prime and Composite Numbers
Divisibility rules
Prime factorization
H.C.F or G.C.F
L.C.M
Application on LCM

From prime factorization to Factors and Multiples

Number System
The text passage provides an explanation of prime factorization, including examples and a practice section with several questions.
multiple_questions

the passage contains multiple questions in the practice section, but no answers are provided for these questions.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Prime Factorization

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

Prime Factorization is the process of expressing a given number as a product of prime factors.

Consider a number say 30. This is a composite number. We can write 30 as

30 = 2 x 15. But 15 is also composite number which can be written as

15 = 3 x 5

∴ 30 = 2 x 3 x 5

When we write 30 = 2 x 3 x 5, none of the numbers 2, 3, 5 are composite numbers.

2, 3, and 5 are prime factors of 30.

Thus we can say that 30 = 2 x 3 x 5 is the prime factorisation of 30.

There are two methods to find the factors of the given numbers.

1) Factor tree

2) Prime Factorisation Method

Factor tree

Example: Factor tree of 72 is given below.

Prime Factorisation Method

Another method to find the factors of the given number. Here also use the prime numbers. So start with 2 ,3,5,7 according to divisibility of the number. If we start with 2 then complete the division by 2 and then consider the next prime numbers.

Express the following as product of prime factors.

1) 150

150 = 2 x 75

= 2 x 3 x 25

= 2 x 3 x 5 x 5

The prime factors of 150 are 2 x 3 x 5 x 5

2) 732

732 = 2 x 366

= 2 x 2 x 183

= 2 x 2 x 3 x 61
_______________________________________________________________
Practice

Using prime numbers, find the factors of the following :
1) 1331
2) 164
3) 729
4) 180
5) 5000
6) 84
7) 91
8) 105
9) 1000
10) 48

Factors and Multiples

Prime and Composite Numbers
Divisibility rules
Prime factorization
H.C.F or G.C.F
L.C.M
Application on LCM

From prime factorization to Factors and Multiples

Number System
user
The text passage provides an explanation of prime factorization, including examples and a practice section with several questions.

TYPE: MULTIPLE_QUESTIONS

The passage contains multiple questions in the practice section, but no answers are provided for these questions.