Factors and Multiples
Lessons in this chapter
About Factors and Multiples
Factors and Multiples is the chapter where numbers stop being quantities and start having structure, which is what the whole of fraction work then depends on.
Interpret Rules of Divisibility of 2, 5 and 10 and Divisibility of 3,6, and 9 give quick tests. The digit-sum rule for 3 and 9 is the surprising one: 4,572 is divisible by 3 because 4 + 5 + 7 + 2 is 18, and that works for any number however long.
Understand Factors and Understand Multiples establish the two directions. Factors divide into a number and are finite; multiples are what the number divides into and go on forever. Kids mix the words constantly, and the finite-versus-endless distinction is the quickest way to keep them apart.
Find Common Factors and Greatest Common Factor and Find Common Multiples and Lowest Common Multiple are the ones with an immediate payoff. The greatest common factor is how you simplify a fraction and the least common multiple is how you add two with different denominators, both of which arrive in the very next chapters.
Understand Prime and Composite Numbers closes it. A prime has exactly two factors, itself and one, which is why 1 is not prime, and primes are the pieces every other number is built from.
All seven lessons open as a 4th grade math worksheet in the page. Understand Factors works through factor pairs, Find Common Factors and Greatest Common Factor and Find Common Multiples and Lowest Common Multiple set the problems that fraction work depends on, and Understand Prime and Composite Numbers closes it. Every question is scored as you answer it, free to try, with no login needed for your first 3.
Frequently asked questions
Interpret Rules of Divisibility of 2, 5 and 10 and Divisibility of 3,6, and 9 give the quick tests, then Understand Factors and Understand Multiples establish the two directions kids most often mix up. Find Common Factors and Greatest Common Factor and Find Common Multiples and Lowest Common Multiple have the immediate payoff in fractions, and Understand Prime and Composite Numbers closes the chapter. Factor pairs, multiples and prime and composite numbers sit in Operations and Algebraic Thinking (4.OA); the greatest common factor and least common multiple go beyond what the Common Core asks at this grade, which puts them in its 6th grade Number System domain (6.NS).
A factor divides into a number, so the factors of 12 are 1, 2, 3, 4, 6 and 12. A multiple is what you get by multiplying it, so 12, 24, 36 and so on. Factors are finite; multiples never end.
Add its digits. If the total is divisible by 3, so is the number. 4,572 gives 4 + 5 + 7 + 2 = 18, which is divisible by 3, so 4,572 is too.
Simplifying fractions. Dividing the numerator and denominator by their GCF reduces a fraction to its simplest form in one step.
Adding and subtracting fractions with different denominators. The LCM is the smallest denominator both will convert to.
Because a prime has exactly two different factors, itself and 1. The number 1 has only one factor, so it does not qualify.