Hi, I'm Dr. Shah. I was the National Lecture Competition winner in 1989 and I'm the maths master at Mathscool. Now, ready for a new way of doing maths? Important technique on division because it's not only used for younger kids but also when you get older, you need to polynomial division and polynomial division uses that same technique. So, we start off with an example, 2558 divided by 12, and I want to do that using long division. So, I start off by writing inside my division 2558 and then outside is the 12. When I'm looking at this, first thing I want to do is cover up so that I only have two digits here, the same that I have there, and so I'm asking myself, how many times does 12 go into 25. How many times does 12 go into 25? Well, the answer is two times because 2 times 12 is 24. So, I write that underneath there and the next thing I'd do is I then subtract, so 25, subtract 24, is one. Now, you see you only have one digit here, so I bring down the next digit to join it, so I have two digits here again and I ask myself the same question. How many times does 12 go into 15? So, the answer this time would be one time, so I write 1 on top of there and the reason is 1 times 12 is 12. Do the same thing, subtract it, 15 subtract 12, gives me 3. Again, I'm left with one digit down here, so I bring down the next digit which is also the last digit, there are no more digits left to bring down to join that. And then I ask myself, how many times does 12 go into 38? And the answer this time is three times because 3 times 12 is 36, and my final subtraction, 38 minus 36 is 2. Now, there are no more numbers to bring down, so this number here is the remainder. It got left over at the end of our division. And so if somebody asks us, what is 2558 divided by 12, we'd say, well, you'd get 213, that's that number on the top there, but there's this little remainder 2 which got left over and couldn't be divided by 12 so I'll put that 2 still to be divided by 12, so 213 and 2/12 which cancels down, of course, to 1/6. 213 1/6 and in this case, because we got a little number left over that couldn't be divided by, it also tells us that the 12 is not a factor of 2558. Okay, let's do another example. This time we're going to do 1845 divided by 15. So, same technique as before, start off with our divided-by bracket, put the 1845 inside the bracket and the 15 goes outside the bracket. So, first thing I have to do is cover up so I'm only looking at two digits because I've only got two digits out here, and I ask myself, how many times does 15 go into 18? The answer is once because one lot of 15 is 15, and then subtract again. 18 subtract 15 gives me 3. Again, I've got one digit here, so I bring down another one from up there to join, and ask myself, how many times does 15 go into 34? And this time, it will go two times and two lots of 15 is 30. Again, do my subtracting, 34 minus 30 is 4 and bring down the last of these digits, 5, and ask myself the same question. How many times does 15 go into 45? And the answer is 3, three lots of 15 is 45, and so this time, when I do the subtraction, there's nothing left over at all. So, there is no remainder. And so when somebody asks me, what is 1845 divided by 15, I can say that the answer is 123 and there isn't any remainder to put back on top of the 15. In other words, 15 is a perfect factor of 1845.

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