# 1.1.01. Natural numbers

#### Dictionaries

Natural numbers - keywords

#### Sinopisis

1. The set of natural nubers and sympolic notation $N=\{ 1, 2, 3, ...\}$.
2. What does it mean that a natural number $d$ is a divisor of a natural number $n$?
3. What does it mean that a natural number $n$ is a multiple of a natural number $d$?
4. Why, instead of divisor you can say factor?
5. What does the abbreviation $d|n$ mean?
• $d$ is a divisor of $n$
• $d$ is a factor of $n$
• $n$ is divisible by $d$
• $n$ is amultiple of $d$
6. Even numbers $0, 2, 4, 6, 8, ...$ nad odd numbers $1, 3, 5, ...$.
7. Division with remainder $n=k\times d+r$
8. Prime numbers: 2, 3, 5, 7, 11, 13, ...
9. Euklides's Theorem ($\infty$)
10. The sieve of Eratosthenes
11. Composite numbers: 4, 6, 8, 9, 10, 12, 14, ...
12. Unique Prime Factorization
13. GCD and LCM
14. Divisibility tests

#### You can do it

Exercise 1. Factorize number 504.
Exercise 2. Factorize number 2250.
Exercise 3. Find GCF(2250,504).
Exercise 4. Find LCM(2250,504).
Exercise 5. Determine whether 7168 is divisible by 2, 3, 4, 5, 6, 8, 9 and 10.