What is the least natural number 2

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Imagine: You have 12 candies and you want to give them to your friends. Of course you share fairly, everyone should get the same amount.



Example: If you have 6 friends, each gets 2 candies. What about different numbers of friends?

Number of friendsNumber of candies
112
26
34
43
5it does not work
62
7it does not work
8it does not work
9it does not work
10it does not work
11it does not work
121


You can divide the number 12 by 1, 2, 3, 4, and 6 and 12. The product of each resulting pair of numbers is 12.

$$1 * 12 = 12$$

$$ 2 * 6 = 12$$

$$ 3 * 4 = 12$$

$$ 4 * 3 = 12$$

$$ 6 * 2 = 12 $$

$$12 * 1 = 12$$

The factors of the products result in the divisors of the number 12.
The divisors are: 1, 2, 3, 4, 6, 12.
Mathematicians use this notation: $$ T_ {12} = {1; 2; 3; 4; 6; 12} $$

If the number of friends is greater than 12, the candies can no longer be divided.

Divider in the picture

You can visualize the divisors of 12 as follows:

$$12*1$$

$$6*2 $$

$$4*3$$

$$ 3*4$$

$$ 2*6 $$

$$1*12$$

Divisors, multiples and prime numbers

So in summary: if you divide a number by its factors, there is no remainder left. The division opens.

If you multiply a number by 2, by 3, by 4, and so on, you get the multiples of the number.

If a number $$ a $$ is a multiple of a number $$ b $$, then the number $$ b $$ is a divisor of the number $$ a $$.


Prime numbers

Then there are numbers that have exactly 2 factors: the 1 and itself.
These are the numbers 2; 3; 5; 7; 11; 13; 17; 19, ...

The number 1 has only one factor (1) and is therefore not a prime number.

If you divide a number by its divisors, there is no remainder left.
A natural number with exactly 2 divisors is called a prime number.
The 1 is not a prime number.

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Find dividers yourself

Find the divisors of the 24th

Write the products $$ \ text {divider} $$ $$ *? = 24 $$ on.

$$1 * 24 = 24$$

$$ 2 * 12 = 24$$

$$ 3 * 8 = 24$$

$$ 4 * 6 = 24$$

$$5$$??
You can't find a natural number for 5 that results in $$ 5 *? = 24 $$. So 5 is not a divisor of 24.

$$6 * 4 = 24$$

You actually already have that with $$ 4 * 6 = 24 $$. If you continue calculating now, the factors will only be reversed. $$ 8 * 3 $$ and $$ 12 * 2 $$ and so on. That means you have already found all the dividers.

The divisors of 24 are: 1; 2; 3; 4; 6; 8th; 12 and 24.
Mathematicians use this notation: $$ T_24 = {1; 2; 3; 4; 6; 8th; 12; 24} $$