Question 989901: find a number that;
The last digit is even
Sum of the digits is divisible by 3
The last 2 digits are divisible by 4
The last digit is 0 or 5
The number is divisible by 2 and 3
The last 3 digits form a number divisible by 8
The sum of the digits is divisible by 9
The last digit is 0
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
| Original Statement | Translation |
|---|
| The last digit is even | 2 is a factor | | Sum of the digits is divisible by 3 | 3 is a factor | | The last 2 digits are divisible by 4 | 4 is a factor | | The last digit is 0 or 5 | 5 is a factor | | The number is divisible by 2 and 3 | 6 is a factor | | The last 3 digits form a number divisible by 8 | 8 is a factor | | The sum of the digits is divisible by 9 | 9 is a factor | | The last digit is 0 | 10 is a factor |
In short, we know this number has the following factors: 2,3,4,5,6,8,9,10
There could be other factors or repeats of those factors above. Let's say that there is only one copy of each and only those factors are there
Multiply out all the factors: 2*3*4*5*6*8*9*10 = 518,400
So the smallest number possible is 518,400 Any other multiple of this number works as well.
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