Solving word problems involving factors and multiples

0:00- [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?

0:18And 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.

0:34Well, 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.

0:54That 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.

1:13That'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.

1:31And 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.

1:514 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.

2:10Or 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.

2:34So 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.

2:53So 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.

3:13Another 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.