How to check if a number is divisible by 14,669
The method
Here is an easy way to determine if a number is divisible by 14,669.
First, multiply the last digit by 1,467. Then, take that number and add it to the remaining digits as if they were a number that is one digit shorter. Then repeat the process until the number is “clearly” divisible by 14,669 or not. This will match whether the original number is divisible by 14,669.
Okay, so maybe not that easy.
There is also another rule for handling numbers greater than a billion that can be speed things up (check the video below).
At least one reputable mathematician calls these the “Oliver Brown tests”.
An examples
Firstly, here are the first 10 multiples of 14,669:
Lets consider the number 3,681,919.
| Number | Last digit × 1,467 | Remaining digits | Result |
|---|---|---|---|
| 3,681,919 | 13,203 | 368,191 | 381,394 |
| 381,394 | 5,868 | 38,139 | 44,007 |
44,007 = 14,669 × 3
therefore 3,681,919 is also divisible by 14,669.
But why
Matt Parker of Standup Maths wrote a Python script to generate divisibility rules for numbers up to 30,000. The above is one of them.
