What is this number?

Question

Here are the clues:
It is an even 3 digit number
It is divisible by 3,4,6,8, and 9.
The sum of it's digits are 18
The difference between the first and second digit equals the third digit.

It's a real hard problem.

Answer 1

It is not a hard problem.The number is 792.If however you are strict that the first digit should be greater than the second one,it is 936

Answer 2

2 (even) = 2
3 = 3
4 = 2 * 2
6 = 2 * 3
8 = 2 * 2 * 2
9 = 3 * 3

The lowest common multiple of all these numbers is 2 * 2 * 2 * 3 * 3 = 72.

So at a minimum the number has to be divisible by 72

The multiples of 72 that are 3 digits long are:
144 - sum is 9
216 - sum is 9
288 - sum is 18, but the difference isn't correct (-6)
360 - sum is 9
432 - sum is 9
504 - sum is 9
576 - sum is 18, but the difference isn't correct (-2)
648 - sum is 18, but the difference isn't correct (2)
720 - sum is 9
792 - sum is 18, but the difference isn't correct* (-2)
864 - sum is 18, but the difference isn't correct (2)
936 - sum is 18, and the difference *is* correct (6) <---

So your answer is 936

Notice also that a - b = c which also means that a = b + c.
Since a + b + c = 18 and b + c = 9, then a must be 9. This confirms the answer of 936.

* Note: I interpret the difference to mean 1st digit - 2nd digit = 3rd digit, not 2nd digit - 1st digit = 3rd digit.

Answer 3

3 digit #'s divisible by 9 & 8 Are multiples of 72. Those whose digits add to 18 are:
288, 576, 648, 792, 864, 936
difference between 1st & 2nd digits =3rd:

792 : 9-7=2 7+9+2=18 792=8*9*11

936 : 9-3=6 9+3+6=18 936=8*9*13

there are 2 solutions: 792 & 936

Answer 4

abc ids the number

a-b=c
a+b+c=18
from these two it follows that 2a=18 thus a = 9.


divisible by 4 : c is one of 0,2,4,6,8 ( then they are also divisible by 6 )

so the possible numbers are
990
972
954
936
918

oinly 936 is ok the other are not divisble by 8

Answer 5

936

Answer 6

936

936 is divisible by 3,4,6,8 and 9
9 minus 3 equals 6
9 + 3 + 6 = 18

i got it right, right?

Answer 7

972