 Let's just move to the rounding of numbers. We can round to the nearest integer using the round function. So let's do a round. So we can call the round function 3.4. And that's going to round, of course, to the floating point value 3.0. It is only at values of 5 that it starts rounding up. So 3.5 is going to round up to 4. Now what we can do is force the issue so that it always rounds towards positive infinity side. And we can do that with a ceiling function, C-E-I-L. So if I put in 3.001, normally that, of course, would round to 3, but I'm forcing the issue so that it rounds to positive infinity side. So that's going to give me a 4. Same with ceiling on the negative number side. So let's take negative 3.999. You know, that's going to, of course, round to negative 4, but I'm forcing it towards the positive infinity side of the real line. So that is going to go to negative 3. I can force it to go to the floor side. Now floor means it's going to go towards negative infinity. So 3.999, which you can think rounds to 4. If I force the issue, it's going to go towards the negative infinity side. The same will go for, say, negative 3.001, which is going to go to negative 4. We're forcing it in that direction. We can go a step further. In Julia, we can also force things towards the zero. And for that, I use trunk, trunc. So if I use 3.999, that's going to go down to the zero side, which is 3. But on the other hand, if I use the truncate or trunk, if I do negative 3.999, it's going to go towards the zero side, which is going to be 3. Let's move on. I just want to show you greatest common divisor and least common multiple. Now the greatest common divider, greatest common divider, there we go, that's a function. So let's take this example that I've put down there, 4, 8, 20. So it's going to look at what can we divide into all of those numbers that will leave us with a zero remainder, with a zero remainder. Of course, I can divide one into each of those. One goes into four, four times. One goes into eight times. One goes into 20. So one would be a common divisor without any remainders, but I want the largest possible one. And it looks like four can go into itself, four can go into eight, and four can go into 20. So indeed four is going to be my greatest common divisor. The least common multiple, on the other hand, let's have a look at that. Least common multiple, let's do the three, the five, the two, the three, the five, and the ten I looked at. Now it's going to take multiples of those. What are multiples of two? Two, four, six, eight, multiples of three. Three, six, nine, et cetera, five. So it's five, ten, fifteen, ten is ten, twenty, thirty. So it's going to plot out all of those, all of those multiples, and it's going to see which one is the smallest common one amongst all of those. So let's have a look at that. It turns a thirty. So for two, we're going to do four, six, eight, ten, until we get to thirty, three, six, nine, twelve, until we get to thirty, five, until we get to thirty, and then ten, twenty, thirty. So ten, of course, is going to play the usual. So from ten, we'll have to go to twenty, because remember, three cannot go into ten without a remainder. Twenty-three, well, three can't go in there. Thirty, yes, they can all go into thirty. That's going to be the smallest common multiple. So those greatest common divisor and least common multiple you can use to create effect in your calculations.