• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • ICSE Solutions
    • ICSE Solutions for Class 10
    • ICSE Solutions for Class 9
    • ICSE Solutions for Class 8
    • ICSE Solutions for Class 7
    • ICSE Solutions for Class 6
  • Selina Solutions
  • ML Aggarwal Solutions
  • ISC & ICSE Papers
    • ICSE Previous Year Question Papers Class 10
    • ISC Previous Year Question Papers
    • ICSE Specimen Paper 2021-2022 Class 10 Solved
    • ICSE Specimen Papers 2020 for Class 9
    • ISC Specimen Papers 2020 for Class 12
    • ISC Specimen Papers 2020 for Class 11
    • ICSE Time Table 2020 Class 10
    • ISC Time Table 2020 Class 12
  • Maths
    • Merit Batch

A Plus Topper

Improve your Grades

  • CBSE Sample Papers
  • HSSLive
    • HSSLive Plus Two
    • HSSLive Plus One
    • Kerala SSLC
  • Exams
  • NCERT Solutions for Class 10 Maths
  • NIOS
  • Chemistry
  • Physics
  • ICSE Books

What Is Fundamental Theorem of Arithmetic

December 15, 2022 by Phani Raju

Fundamental Theorem of Arithmetic

We have discussed about Euclid Division Algorithm in the previous post.

Fundamental Theorem of Arithmetic:
Statement: Every composite number can be decomposed as a product prime numbers in a unique way, except for the order in which the prime numbers occur.
For example:
(i)  30 = 2 × 3 × 5, 30 = 3 × 2 × 5, 30 = 2 × 5 × 3 and so on.
(ii) 432 = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 24 × 33
or 432 = 33 × 24.
(iii) 12600 = 2 × 2 × 2 × 3 × 3 × 5 × 5 × 7
= 23 × 32 × 52 × 7

In general, a composite number is expressed as the product of its prime factors written in ascending order of their values.
Example: (i) 6615 = 3 × 3 × 3 × 5 × 7 × 7
= 33 × 5 × 72
(ii) 532400 = 2 × 2 × 2 × 2 × 5 × 5 × 11 × 11 × 11

Fundamental Theorem of Arithmetic Example Problems With Solutions

Example 1:    Consider the number 6n, where n is a natural number. Check whether there is any value of n ∈ N for which 6n is divisible by 7.
Sol.    Since,   6 = 2 × 3; 6n = 2n × 3n
⇒ The prime factorisation of given number 6n
⇒ 6n is not divisible by 7.

Example 2:   Consider the number 12n, where n is a natural number. Check whether there is any value of n ∈ N for which 12n ends with the digit zero.
Sol.     We know, if any number ends with the digit zero it is always divisible by 5.
If 12n ends with the digit zero, it must be divisible by 5.
This is possible only if prime factorisation of 12n contains the prime number 5.
Now, 12 = 2 × 2 × 3 = 22 × 3
⇒ 12n = (22 × 3)n = 22n × 3n
i.e., prime factorisation of 12n does not contain the prime number 5.
⇒ There is no value of n ∈ N for which 12n ends with the digit zero.

Filed Under: Mathematics Tagged With: Fundamental Theorem of Arithmetic, Fundamental Theorem of Arithmetic Examples, Real Numbers

Primary Sidebar

  • MCQ Questions
  • RS Aggarwal Solutions
  • RS Aggarwal Solutions Class 10
  • RS Aggarwal Solutions Class 9
  • RS Aggarwal Solutions Class 8
  • RS Aggarwal Solutions Class 7
  • RS Aggarwal Solutions Class 6
  • ICSE Solutions
  • Selina ICSE Solutions
  • Concise Mathematics Class 10 ICSE Solutions
  • Concise Physics Class 10 ICSE Solutions
  • Concise Chemistry Class 10 ICSE Solutions
  • Concise Biology Class 10 ICSE Solutions
  • Concise Mathematics Class 9 ICSE Solutions
  • Concise Physics Class 9 ICSE Solutions
  • Concise Chemistry Class 9 ICSE Solutions
  • Concise Biology Class 9 ICSE Solutions
  • ML Aggarwal Solutions
  • ML Aggarwal Class 10 Solutions
  • ML Aggarwal Class 9 Solutions
  • ML Aggarwal Class 8 Solutions
  • ML Aggarwal Class 7 Solutions
  • ML Aggarwal Class 6 Solutions
  • HSSLive Plus One
  • HSSLive Plus Two
  • Kerala SSLC

Recent Posts

  • Difference Between G And g: A Comprehensive Guide
  • Difference Between Isotopes And Isobars: Understanding The Key Differences
  • Difference Between Biodegradable And Nonbiodegradable: A Comprehensive Guide
  • Difference Between Fragmentation And Regeneration: Understanding The Key Differences
  • Difference Between Flora And Fauna: A Comprehensive Guide
  • Wireless Network Advantages and Disadvantages | Advantages and Disadvantages of Wireless Network Communication
  • Franchising Advantages and Disadvantages | Pros and Cons of Buying a Franchise, Advantages and Disadvantages
  • Spiral Model Advantages and Disadvantages | Advantages and Disadvantages of Using Spiral Model
  • Advantages and Disadvantages of Prototype Model | Prototyping Model in Software Engineering for Testing
  • Interviews Advantages And Disadvantages | What is an Interview? 6 Merits and Demerits of Interview
  • Advantages and Disadvantages of Observation Method | Merits and Demerits of Observation in Marketing

Footer

  • RS Aggarwal Solutions
  • RS Aggarwal Solutions Class 10
  • RS Aggarwal Solutions Class 9
  • RS Aggarwal Solutions Class 8
  • RS Aggarwal Solutions Class 7
  • RS Aggarwal Solutions Class 6
  • Picture Dictionary
  • English Speech
  • ICSE Solutions
  • Selina ICSE Solutions
  • ML Aggarwal Solutions
  • HSSLive Plus One
  • HSSLive Plus Two
  • Kerala SSLC
  • Distance Education
DisclaimerPrivacy Policy
Area Volume Calculator