# What is the least natural number 2

### Share with friends

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 friends | Number of candies |
---|---|

1 | 12 |

2 | 6 |

3 | 4 |

4 | 3 |

5 | it does not work |

6 | 2 |

7 | it does not work |

8 | it does not work |

9 | it does not work |

10 | it does not work |

11 | it does not work |

12 | 1 |

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: $$ T_24 = {1; 2; 3; 4; 6; 8th; 12; 24} $$

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