8, since 946 is not so. A number is divisible by 3 or 9 only when the sum of its digits is divisible by 3 or 9. Take for example 1234; this is
| 1 thousand, | or | 999 and 1 | |
|---|---|---|---|
| 2 hundred, | or | twice 99 and 2 | |
| 3 tens, | or | three times 9 and 3 | |
| and | 4 | or | 4 |
Now 9, 99, 999, &c. are all obviously divisible by 9 and by 3, and so will be any number made by the repetition of all or any of them any number of times. It therefore depends on 1 + 2 + 3 + 4, or the sum of the digits, whether 1234 shall be divisible by 9 or 3, or not. From the above we gather, that a number is divisible by 6 when it is even, and when the sum of its digits is divisible by 3. Lastly, a number is divisible by 5 only when the last figure is 0 or 5.
- Where the divisor is unity followed by ciphers, the rule becomes extremely simple, as you will see by the following examples:
- 100) 33429 (334
- 300
- 342
- 300
- 429
- 400
- 29
This is, then, the rule: Cut off as many figures from the right hand