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