What number is divisible by 871?

Meinstein

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

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The number is ...

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

45The 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.
 115The number is divisible by 5 but not by 15.