4 th Grade Math Factors and Multiples Topic Overview

factors and multiples factors are numbers that divide given number without remainder for example let's find the factors of 24 we know that 1 times 24 is 24 so both 1 and 24 go into 24 evenly 2 times 12 equals 24 so that means 2 and 12 are factors 3 times 8 is 24 so their factors 2 4 times 6 5 times 5 times nothing 5 times nothing is 24 it doesn't go into 24 evenly so get out of here five we already listed six seven seven times nothing is twenty-four there we have all the factors next let's find the factors of 45 we know that 1 times 45 is 45 so both 1 and 45 go into 45 evenly 2 times nothing is 45 it doesn't go into 45 evenly so get out of here 2 3 times 15 equals 45 so that means 3 and 15 are factors four times nothing is 45 bye bye four five times nine is 45 so their factors two six seven and eight they don't go into 45 so they're out of here so there we have it here's our list of factors of 45. let's try some of these examples determine whether 28 is multiple of 7 well if we divide 28 by 7 it equals 4 that means it goes in evenly so the answer is yes the second example says determine whether 49 is multiple of 8 well if we divide 49 by 8 it goes in 6 times but that's only 42 and then there's remainder of 7 so it doesn't go in evenly therefore 49 is not multiple of 8. the least common multiple is the smallest multiple that two numbers have in common let's look at example one what is the least common multiple of two and three let's list the multiples of 2. 2 4 6 8 10 12 and so on but let's stop here for minute the multiples of 3 are 3 6 6 6 is on the list for two so since the first multiple they have in common is 6 the least common multiple is 6. let's check out example 2. what is the least common multiple of 6 and 8 let's list the multiples of 6 6 12 18 24 30 36 and so on let's check out 8 8 16 24 hey look 24 was in the multiple list of six too it's the first multiple they have in common so the least common multiple must be 24. the greatest common factor is the largest factor that divides two numbers for example what is the greatest common factor of twelve and sixteen well let's list the factors of twelve one and twelve two and six and three and four now let's list the factors of sixteen one and sixteen two and eight and four and four they have few common factors one two and four but which one is the greatest it's four so the greatest common factor of twelve and sixteen is four now you're ready to try some problems about factors good luck