# What number is divisible by 871?

## Meinstein

The Divisibility rules for natural numbers show quickly whether and how a natural number can be divided.

### regulate

The number is ...

 divisible by Divisibility rule 2 if its last digit is a 0 or an even number. 3 if the checksum is divisible by 3, 4 if its last two digits result in a number that is divisible by 4. 5 if its last digit is a 0 or 5, 6 if the number is divisible by 2 and by 3 7 see below. 8 if the number formed from the last three digits is divisible by 8. 9 if your checksum is divisible by 9 10, 100, 1000… if your last digit is 0, 00, 000…. 11 see below 12 if the number is divisible by 3 and by 4. 15 if the number is divisible by 3 and by 5. 25 if the number from the last two digits is divisible by 25. 30 if the last digit is a zero and is divisible by 3 without this last digit. 40 if the last digit is a zero and is divisible by 4 without this last digit. 50 if the last digit is a zero and without this is divisible by 5. 125 if the number from the last three digits is divisible by 125.

### Divisible by 7

We divide the number into two parts: b is the last digit, a are the digits in front of it.

8715 → 871 (a) and 5 (b)

We subtract b from a two times:

871 – 10 = 861

We repeat this process until we get a number that we can figure out in our head whether it is divisible by 7.

86 – 2 = 84

Since 84 is divisible by 7, it's 8715 too.

### Divisible by 11

A number is divisible by 11 if the alternating checksum is divisible by 11.

### Exercises

 45 The 5 indicates that the number is divisible by 5. Since the checksum is 9, 3 is also a factor. So 45 is also divisible by 15. 115 The number is divisible by 5 but not by 15.