# If the 5 digit number #1364"?"# is divisible by #3# then what are the possible values of the last digit?

##### 1 Answer

#### Explanation:

In the decimal number system that we use, an integer is divisible by

#1+3+6+4+color(blue)(1) = 15# is divisible by#3# .

So

#1364color(blue)(1)+3 = 1364color(blue)(4)#

and

#1364color(blue)(4)+3 = 1364color(blue)(7)#

**Footnote**

Why does this method of checking the digits add up to a multiple of

Essentially because when you divide

So for example:

#color(red)(153) = (100*color(red)(1)) + (10*color(red)(5)) + (1*color(red)(3))#

#= (99+1)*color(red)(1) + (9+1)*color(red)(5) + (0+1)*color(red)(3)#

#= (99*color(red)(1) + 9*color(red)(5) + 0*color(red)(3)) + (1*color(red)(1) + 1*color(red)(5) + 1*color(red)(3))#

#= 3(33*color(red)(1) + 3*color(red)(5) + 0*color(red)(3)) + (color(red)(1)+color(red)(5)+color(red)(3))#

The expression

So we find that