4 th Grade Math Factors and Multiples Determining the Difference

hi so today we want to look at the difference between factor and multiple and distinguish between the two of those i'll give some examples and hopefully by the end of this video you'll understand this key these two key terms lot better factors are the two numbers that are being multiplied in order to get product now multiple it is the product of the two given factors so let's look at the number six when we write the factors for six if you do it in this way in writing them out when you finish you'll have them in sequential order so what times six is six one times six is there anything times two sure two times three is six now keep going and let's see if there's any other factors is there anything times four that will equal six no what about times 5 no right so when you get to 6 you're back to 6 and of course we already have 6 listed as factor so there's no reason to go further so these are your factors of 6 and they're written in order 1 2 3 and 6. all right so now let's look at larger number let's look at 18. when we list the factors for 18 we still want to start with the same starting with number one let's list starting with one all the factors for eighteen one times eighteen two two times what two times nine is there anything times three sure three times six what about four four times anything not anything times four is there what about five five times anything to get to eighteen no what about six sure six six times three but it's already listed you see so here are all the numbers that are factors for 18 and if you were to rewrite those you could pull this together and that would be an order okay so let's look at the number 32. when we list the factors for 32 we'll start in the same way always start with one one times 32 2 2 times what well we know that 2 times 15 is 30 2 times 16 is 32 anything times 3 times 3 3 times 10 is 30 and 3 times 11 is goes over it's 33 so we're not going to use 3 as factor what about times 4 4 four times eight yeah so when you know your multiplication facts this really helps you out what about times five anything times five no what about times six anything times six no what about seven no and when you get to eight it's already listed okay so here are all your factors for 32 and they're listed in order from least to greatest now let's take look more at multiples all right so now let's take look at multiples multiple is the actual product of two factors so let's give an example let's start with six okay so we could continue on because actually if you mult multiplied six and you continued times seven times eight it's really infinite you could continue on into the millions and find multiples of six here are the multiples that we've written so far of six so you may notice that when you are listing out multiples this is just skip counting and so you don't have to write them out like this you can just actually do your skip counting like this and list them out in this way and it goes lot faster you might be asked the question is 43 multiple of six so in order to determine that you might want to continue your pattern to at least get up to that point of 43. so let's continue on so now we've passed 43 haven't we so 43 is somewhere in between here so could we answer the question is 43 multiple of 6 it's not is it 42 is multiple 48 is multiple but not 43 44 45 46 or 47 okay so just continue the pattern out pass the number that you're asked to determine whether it is multiple or not and you'll be able to see that so in this example it says to select all the multiples of nine remember the definition or the meaning of multiple is the multiples are the actual products and so when you have factor such as nine you need to multiply it times another factor in order to get to one of these multiples so what times nine is sixty-two well we know that nine times seven is sixty-three so this is not going to work is there something times 9 that equals 9 times 6. so here's one that we would select 39. although this has 9 in the actual answer here 30 with 9 it's not multiple of 9 there's no way to multiply 9 to get 2 39 so this is not correct is 9 multiple of 9 absolutely absolutely one times nine okay and then what about 28 it's close isn't it but 9 times 3 is 27 so here's your last one that is actually multiple of 9. hope this video helped you let's just quickly recap multiples are the actual products of factors and it's like skip counting skip counting like with 5 5 10 15 20 and so forth factors are the two numbers that you multiply to get two particular number one times ten these two numbers are the factors of ten also two times five and in this video showed you how to write them out in sequential order by saying 1 times 10 and 2 times 5 so that they're placed in order from least to greatest but either way you know that these are the factors for the number 10. hope this video has helped you in determining the difference between multiples and factors thanks for watching you