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Prime factorization (European method) – Introduction – pg. 1/4

Posted in Math Theory by Lia on 06/05/2014

pg. 1, 234

Contents:

pg. 1….. Prime factorization (European method) – Introduction 

pg. 2…..Prime factorization (European method) – Examples

pg. 3….. Prime factorization (European method) – Exercises

pg. 4…..Prime factorization (European method) – Answers to exercises

1. Introduction to Prime factorization

Factors of a number or expression, are numbers or expressions that divide evenly into the original number or expression.

 

This post will explain the prime numbers’ factorization only.

 

prime number is an integer that can be divided only by itself and by 1.

Example: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 and so on.

 

Prime factorizing a number is equivalent, to finding all the prime numbers and their multiple, that are factors of that number.

 

Any number that is an integer and is not a prime number, can be written as a product of prime numbers. 

 

 Below are a few useful facts about small prime numbers.

  • Numbers that are divisible by 2.

Any number that ends in  0, 2, 4, 6 or 8 (is an even number) is divisible by 2.

Example of numbers divisible by 2: 

10 ends in 0; 12 ends in 2;  374 ends in 4; 2436 end in 6; 25468 ends in 8.

  • Numbers that are divisible by 3.

Any number that has the sum of its individual digits divisible by  3 is divisible  by 3.

Example:  

*  354: 3 +5 +4 = 12; 12 is divisible by 3 therefore, 354 is divisible by 3  ({354/3} = 118).

*  2547: 2 +5 + 4 + 7 = 18; 18 is divisible by 3 therefore 2547 is divisible by 3     

({2547/3} = 849).

  • Numbers that are divisible by 5.

Any number that ends in 0 or 5 is divisible by 5.

Example:

*  120 ends in 0 therefore, 120 is divisible by 5;  

*  235 ends in 5 therefore, 235 is divisible by 5.

 

pg. 1, 234

 

 

 

 

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