Solving word problems involving factors and multiples

- [Instructor] We are
told glue sticks are sold

in packs of 6 and packs of 4.

Mr. Ramiro wants to buy
glue sticks for 28 students.

It's okay with him to purchase extras.

So the first question is,

if Mr. Ramiro chooses the
packs of 6 glue sticks,

how many packs should he buy?

And the second question,

if Mr. Ramiro chooses the
packs of 4 glue sticks,

how many packs should he buy?

So pause this video and have a
go at both of these questions

before we do this together.

All right, now let's tackle

this first question right over here,

if we have packs of 6 glue sticks.

Well, one way to think about
it is we could just say,

all right, if I have one pack that's 6.

If I get another pack, that's another 6.

How many do I have right now?

Well, that's a total, actually,

let me just write it this way.

Maybe I'll say packs.

We have 1, 2, 3, 4, 5, 6.

That should be enough.

And then let's say the total sticks,

the total number of glue sticks.

So if he buys 1 pack,

he's going to have 6 glue sticks.

That's not enough.

So 2 packs, he's gonna add 6 to that.

So that's 12 glue sticks.

You might recognize that as 2 times 6.

That's still not enough.

We still don't have 28.

So let's add another 6.

That's 3 packs, we get to 18.

I'm just adding 6 each time.

Let's add another 6,

because we're still not at 28 yet.

We get to 24 and 4 times 6 is 24.

We're still not at 28 yet.

So now let's add another 6.

And we get to 30 because 5 times 6 is 30.

So what I've just listed
over here are multiples of 6.

And that makes sense

because for every pack
I have exactly 6 in it.

Now we see that 30 is more than
enough for the 28 students.

So 5 packs is how many Mr.
Romero would have to buy.

4 would not be enough.

because that only gets us to 24 packs.

Now there's something
interesting about 30.

It doesn't get us exactly to 28.

So we have a remainder here.

We have a remainder.

We have 2 extra glue sticks.

And that's because 28
is not a multiple of 6.

Or another way to think about it is

6 is not a factor of 28.

So we're gonna have to overshoot,

we're gonna have to
buy a little bit extra.

Now let's think about the
situation when we have packs of 4.

So I'll do the same thing.

Packs 1, 2, 3, 4, 5, 6, 7, 8.

And now let's see the
total number of sticks.

So 1 pack, we're talking
about the packs of 4 now,

that's gonna be 4.

2 packs is 8.

I'm just counting up by 4.

3 packs is 12.

I'm just adding 4 each time.

4 packs is 16.

You could also think about 4
packs of 4 is 4 times 4 is 16.

If I have 5 packs, I'm
gonna add 4 to that.

So what I'm really doing is

listing all the multiples of 4.

I'm increasing multiples
of 4, still not at 28.

Well, I'm gonna add 4 more, I get to 24.

Still not there.

Add 4 more, I get to 28.

That is looking good.

That is exactly 7 packs.

And we know that if we
think about it this way too,

7 times 4 is equal to 28.

Another way to think about
it is because if I take 4

and I multiply it times
a whole number like this,

I get a multiple of 4.

So 28 is a multiple of 4,
or 4 is a factor of 28.

And then I would buy exactly
how many I need with no extra.