Also applies for checking the divisibility by its factors?

[Quant Warrior]

Can I say that divisibilty rule for the factors of a number is the same as for the number itself ?

For example: If we want to find out whether a number "abcdefg" is divisible by 999. We will make triplets of numbers from right and then add them if the sum of triplets is divisible by 999. Then the number itself will be divisible perfectly by 999.

Like this: (efg + bcd + 00a)/999

Now second part of my question: 27 and 37 are factors of 999. Suppose we want check if the same number "abcdefg" is divisible by 27 or 37. Can we apply the same rule for testing the divisiblity of 27 and 36 that we did for 999?

Regards

 

[HallsofIvy]

IF a number is divisible by 999 then of course it is divisible by both 27 and 37. If it is divisible by both 27 and 37 then it is divisible by 999. But a number might be divisible by either 27 or 37 without being divisible by 999, in which case the test for divisibility by 999 would not work. For example 102675= 37(2775) has "triplets" 675+ 102= 777 which is not divisible by 999.