00:01
Let's talk about prime factorization.
00:03
We want to start with the number 27.
00:05
That's going to break down into 3 cubed.
00:09
So we want a multiple of 27 that has exactly 70 factors.
00:14
Well, that means we're going to have 3 to the 70th power.
00:18
That 27 is going to be included in there.
00:21
So that's going to be our answer.
00:22
We're not going to multiply it out.
00:25
So now we want to know the digits that will make this true.
00:28
So we have 6 as a factor of 4, 3, 8.
00:31
Blank seven.
00:33
So we need a six.
00:34
Four is a factor of three, six, a six.
00:39
Okay, then we're going to have three is a factor of five, three, blank one.
00:45
And then we're going to have nine as a factor of seven blank three, four, two, six, four.
00:53
And then we'll get to the next one.
00:56
So for six, we need to have, of that ends in an eight.
01:01
I'm glad.
01:02
Because for six, we have to have an even number, which we do, and then the sum of the digits has to be equal to a multiple of three.
01:10
So let's add up our digits.
01:12
We're going to have 7, 15, 30, so that it adds to be 30.
01:16
So what can i put in this blank so that i can still have a number that would add to be a multiple of three? i could add a zero because we'd have 30.
01:26
I could add a 3, 33, 36, or 39.
01:30
So there we would have our multiples of 3.
01:34
So let's go to this third one here and do the same thing, because i can say 5 plus 3 plus 1 equals 9.
01:42
So what can i put in that blank to end up being divisible by 3? the same thing, 0, 3, 6, or 9.
01:50
I want to go and go to the fourth one because we'll do the same thing.
01:54
Add my digits 10, 26.
01:56
Now for these to be a multiple of 9, when we have to add a digit so that it's divisible by 9.
02:04
So i could say 26 plus 1 would be divisible by 9.
02:08
Then the next number divisible by 9 would be what? 36.
02:13
Well, there's no way i can add a digit to get 36.
02:16
So one would be my only answer.
02:19
If i look at this one, divisible by 4.
02:21
When you're divisible by 4, you only look at the first or the last two digits.
02:26
Those last two digits have to be divisible by 4.
02:30
So i'm going to think, what could i put in front of a 6? that would be divisible by four.
02:35
Well, i could put a 1, 16.
02:39
Can i put anything else? yep, i can put a 3...