In today's video, we're going to look at what multiples and factors are. If we start with multiples, these are basically the times tables of a number. So the first five multiples of six are six because that's 1 * 6, 12 because that's 2 * 6, 18 because that's 3 * 6 and so on. So the next ones would be 24 and 30. Because of this, all the multiples of a number will be divisible by that number without any remainder. For example, 18 / 6 is 3 with no remainder. So 18 must be a multiple of six. Whereas if we looked at 19, 19 / 6 is 3 with a remainder of one. So it's not a multiple of six because it gave a remainder. We can use this rule to check if really big numbers are multiples of a certain number. For example, if we wanted to check whether 378 and 412 were multiples of 6, all we need to do is divide them both by 6. 378 / 6 is 63. So because 63 is a whole number, 378 must be a multiple of 6. 412 / 6 though is 68.6 recurring, which isn't a whole number. So 412 can't be a multiple of six. Another way to think about the multiples of a number is to just keep on adding that same number. So to find the multiples of 14, we could just keep adding 14 to get 28, 42, 56, 70 and so on. And all of these numbers that we get would be the multiples of 14. Now the best way to understand factors is to start with factor pairs. If we had the number 28, then its factored pairs would be the pairs of whole numbers that can be multiplied together to make 28. So 2 * 14, 4 * 7, and 1 * 28. And it's these six numbers that make up these factor pairs that would be the factors of 28 because they're all whole numbers that can be multiplied by another whole number to make 28. Another way to think about the factors of a number are all the numbers that divide into it a whole number of times. For example, four is a factor of 28. because 28 / 4 is 7 which is a whole number. Whereas 5 isn't a factor because 28 / 5 is 5.6. So five doesn't go into it a whole number of times. If you want to quickly find all the factors of a number, the best thing to do is write out all the factor pairs. Starting with 1 * the number itself. So if we wanted to find all the factors of 48, we'd start with 1 * 48, then do 2 * whatever factor is needed to make 48, so 24, and so on with 3 * 16, 4 * 12. 5 doesn't go into 48, so isn't a factor. Then we have 6 * 8. 7 also isn't a factor. And then we get to 8, which we've actually already covered in 6 * 8. So we can stop here. And we know that our factors in ascending order are 1 2 3 4 6 8 12 16 24 and 48. So to find all the factors of 50, we're to do 1 * 50, 2 * 25, 3 doesn't go into 50, four also doesn't work, 5 * 10, 6, 7, 8, and 9 don't work. And then we're at 10, which we've already done. So the factors are just 1 2 5 10 25 and 50. So to quickly sum everything up, if we took a number like 12, its multiples would be the bigger numbers that it can multiply to like 24, 36, 48, and so on. Whereas its factors are the numbers it can be divided into like 1 2 3 4 6 and 12. Just make sure that you remember which one is which because it's really easy to get them the wrong way around in exam. And also remember that the number itself counts as both a multiple and a factor. So 12 is in both of these lists. Anyway, that's everything for this video. So, hope you enjoyed it and we'll see you next time.