# 1 5 is an even number

### Divisible by 2?

Paul is tidying up his closet and sorting his socks. Unfortunately he only found 21 socks. So he knows that a pair of socks is not complete.

So 21 cannot be divided by 2.

Paul's mother comes into the room and is happy that Paul is tidying up. She brings him 3 socks.

Paul laughs. Now all pairs should be complete! Because 24 is an even number and divisible by 2.

A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8.

All even numbers are divisible by 2.

A pair always consists of two identical parts.

### Even or odd?

There was a reason for cleaning up: It's Paul's birthday the next day and he's inviting his friends over. Murat comes first. Then come Finja and Mark. Finally, there is Paul's girlfriend Elena. In total they are now 5. Paul has noted the number of his guests:

additional persons | task | property |
---|---|---|

Murat | 1+1 = 2 | odd + odd = even |

Finja, Mark | 2 + 2 = 4 | straight + straight = straight |

Elena | 4+1 = 5 | even + odd = odd |

- If you add two even or odd numbers, the result is even.
- If you add an even and an odd number mixed up, the result is odd.

### Paul's party can begin

All in all, there are now five of them at Paul's birthday party.

A plate and a cup are set for drinking coffee. Well lie **10 things** on the table.

Paul quickly fetches a saucer for everyone. Well lie **15 things** on the table.

Paul quickly covers forks. Now lie **20 things** on the table.

The numbers 10, 15 and 20 are divisible by 5.

A number is divisible by 5 if its last digit is a 0 or a 5.

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### Every birthday also needs prizes

Paul and his four guests play a lot of games on the birthday. At the end of the first round, everyone has won 2 prizes. 10 prizes went away.

In the second round of the game everyone has won two more prizes. Now all 20 prizes have been awarded.

The numbers 10 and 20 are divisible by 10.

A number is divisible by 10 if its last digit is 0.

If a number has a 0 as the last digit, it can be divided by both 2 and 5. This is why a number is divisible by 10 if it is divisible by 2 and also by 5.

### The secret of the last two digits

Paul's mother gave 4 prizes to each of the 4 guests. That's a total of 16 gifts.

So 16 is divisible by 4.

How can you tell if a number is divisible by 4?

The number 6 cannot be divided by 4. The number 16 does. The number 116 is also divisible by 4. Because **116 : 4 = 29** .

A number is divisible by 4 if its last two digits are divisible by 4.

**Examples:** $$116$$

from 1 | from 26 |
---|---|

$$ 1 cdot 4 = $$ | $$ 26 cdot 4 = 10 $$ |

$$ 2 cdot 4 = $$ | $$ 27 cdot 4 = 10 $$ |

$$ 3 cdot 4 = $$ | $$ 28 cdot 4 = $$$$ 1 $$ |

$$ 4 cdot 4 = $$ | $$ 29 cdot 4 = $$$$ 1 $$ |

$$ 5 cdot 4 = $$ | $$ 30 cdot 4 = $$$$ 1 $$ |

As you can see, they are the last

always divisible by 4.

### The connection between 4 and 25

To see if a number is divisible by 4, look at the last two digits of a number. These last two digits, which are divisible by 4, can be 25 different numbers: from 00, 04, 08, 12, 16… 88, 92, 96.

For the 25 it is exactly the opposite. You check whether the last two digits are divisible by 25. That is, the numbers end in: 00, 25, 50 or 75.

A number is divisible by 25 if its last two digits are 00, 25, 50, or 75.

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### Divisibility rules at a glance

These are the divisibility rules for 2, 5 and 10 and for 4 and 25:

- A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8.
- A number is divisible by 5 if its last digit is a 0 or a 5.
- A number is divisible by 10 if its last digit is 0.
- A number is divisible by 4 if its last two digits are divisible by 4.
- A number is divisible by 25 if its last two digits are 00, 25, 50, or 75.

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