00:01
For this problem, we're supposed to fill in the blank with the smallest digit that will make these numbers divisible by whatever we're looking for.
00:13
So, for the first one, we're looking for the smallest number i can put in these blanks that will make the number divisible by five.
00:22
Okay, so there are divisibility rules for all these.
00:28
The rule for five is that the last digit has to be either zero or five.
00:42
So, i'm looking for the last digit in all these.
00:44
So, if i want it to be divisible by five and the smallest one, all i have to do is put a zero in each one.
00:54
Okay, the rule for three says to add the digits of the number and that sum that you get has to be divisible by three.
01:12
Okay, so for one, four, three, one plus four is five plus three is eight.
01:19
Eight is not divisible by three, but nine is.
01:23
So, if i'll put a one right there, i've got one plus one is two plus four is six plus three is nine.
01:30
So, that's divisible by three.
01:32
Okay, for the next one, four plus seven is twelve.
01:37
Nope.
01:37
Four plus seven is eleven plus five is sixteen.
01:44
Sixteen is not divisible by three.
01:47
Sixteen is not.
01:48
If we add to one, that's seventeen.
01:52
It's not.
01:53
If i put a two in there, that's eighteen and eighteen is divisible by three.
01:59
So, i have to put a two there.
02:01
And the last one, three plus one is four plus six is ten.
02:08
Ten is not.
02:09
If i put a one, that would be eleven and that's not.
02:13
But if i put a two, that is twelve and twelve is divisible by three.
02:21
Okay, for six, first of all, it has to be even.
02:26
If it's not an even number, it's not even divisible by six.
02:30
And then, it has to be divisible by three.
02:34
And remember our rule for three to add the digits.
02:38
So, it has to be even.
02:40
Alright, that eight, that's an even number.
02:44
So, let's see how we can make this divisible by three.
02:46
Just like we did the one in the previous line.
02:51
So, four plus two is six plus eight is fourteen.
02:56
Fourteen is not.
02:58
But if i put a one here, that's fifteen and fifteen is.
03:02
So, it's even and it's divisible by three.
03:06
So, that's good.
03:08
Okay, this one is even.
03:10
So, let's add the digits we've got so far...