+885 Which digit should replace A in the units place of the number 987,654,32A so that the number is divisible by 6?
+4622 Divisible by 6, means divisible by 2 and 3.
Divisible by 2: Even units digit
Divisible by 3: Sum of digits must be divisible by 3.
We have 0,2,4,6,8 for the possibilities for being divisible by 2:
For the divisibility of 3, let's add the values up: 9+8+7+6+5+4+3+2=44
Since the divisibility of 2, means an even units digit, we have:
44+0=44
44+2=46
44+4=48
44+6=50
44+8=52
These values are divisible by 2 (for sure), but we need to check if they're divisible by 3.
44=4+4=8, not divisible by 3
46=4+6=10, not divisible by 3
48= 4+8=12, it is divisible by 3 (yes!)
50=5+0=5, not divisible by 3
52=5+2=7, not divisible by 3
We have one possible value, which is 48.
Thus, our answer is \(48-44=\boxed{4}\)
+129852 Thanks, tertre!!!....here's one more method
If the number is even and the sum of its digits is divisible by 3, it will be divisible by 6
Thus...we can ignore any digit, or sums of digits in the number that are themselves divisible by 3
So...we can ignore the leading 9, the 87 that follows, the 6, the 54 that follows and the 3
So...we' are left with 2A
This is only divible by 6, if A is even and the sum of 2 + A is divisible by 3
Thus....2 + 4 = 6 is the only possibility.....so....A = 4
