Lia's Math – Home page

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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.

 

A 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  ().

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

().

• 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.

 

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