SOLUTION: 476**0 is divisible by both 3 and 11. The non-zero digits in the hundreds and tens places are respectively ? and ?.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: 476**0 is divisible by both 3 and 11. The non-zero digits in the hundreds and tens places are respectively ? and ?.      Log On


   

Question 1009437: 476**0 is divisible by both 3 and 11. The non-zero digits
in the hundreds and tens places are respectively ? and ?.
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
476**0 is divisible by both 3 and 11. The non-zero digits
in the hundreds and tens places are respectively ? and ?.
It has to be divisible by 10 because it ends in a 0
It is divisible by 3 and 11, which are both prime, 
so it has to be divisible by 10*3*11 = 330.

The most it could be is 476990
The least it could be is 476110, since the digits aren't 0.

476990/330 = 1445.424242...
476110/330 = 1442.757575...

So the number divided by 330 is between those,

So the number divided by 330 is either 1443, 1444 or 1445

So the number is either 

1443*330 = 476190
1444*330 = 476520, or
1445*330 = 476850

So there are three different possible answers,

476190, 476520, and 476850

Edwin