Yes.
In order to test for divisibility by 9, the rule of thumb states that the sum of the digits of the number must be divisible by 9. If so, the original number is divisible by 9. For 432, we review as follows:
4 + 3 + 2 = 9; since 9 is always divisible by itself, 432 is also divisible by 9.
For the long way, we can do the math as follows:
48
9|432
36
---
72
72
---
0
So, 432 / 9 = 48
One can also carry the rule of thumb further by summing digits until one arrives at either 9 or a single-digit not equal to 9.
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To be divisible by 2 the number must be even, that is its last digit must be 2, 4, 6, 8, or 0; the last digit of 432 is 2 which is one of {2, 4, 6, 8, 0} so 432 is even and divisible by 2. To be divisible by 3 sum the digits of the number; if this sum is divisible by 3 then the original number is divisible by 3. The test can be repeated on the sum until a single digit remains, in which case if this single digit is 3, 6, or 9 then the original number is divisible by 3; For 432: 4 + 3 + 2 = 9 which is one of {3, 6, 9} so 432 is divisible by 3. To be divisible by 5 the last digit must be a 0 or 5; the last digit of 432 is a 2 which is not 0 nor 5, so 432 is not divisible by 5. To be divisible by 6, the number must be divisible by both 2 and 3; these have been tested above and found to be true, so 432 is divisible by 6. To be divisible by 9 sum the digits of the number; if this sum is divisible by 9 then the original number is divisible by 9. The test can be repeated on the sum until a single digit remains, in which case if this single digit is 9 then the original number is divisible by 9; For 432: 4 + 3 + 2 = 9 which is 9 so 432 is divisible by 9 To be divisible by 10 the last digit must be a 0; the last digit of 432 is a 2 which is not 0, so 432 is not divisible by 10. 432 is divisible by 2, 3, 6 and 9, but not divisible by 5 nor 10.
The digital root of 432 is 9 so the number is divisible by 3. The number formed by the last two digits, 32, is divisible by 4 (4*8) so 432 is divisible by 4.
No, but 432 is divisible by 2 and 3.
No.
The multiples of 432 (which are infinite) are all divisible by 432, including these: 432, 864, 1296, 1728, 2160, 2592, 3024 . . .