Chapter 3
Factors and Multiples
Line up 24 chairs and you can build equal rows several ways: two rows of twelve, three of eight, four of six. Try it with 23 chairs and nothing works except one long row. Both are ordinary numbers, yet they behave completely differently the moment you split them up. What divides a number evenly, its factors, says more about that number than its size does. Some numbers are packed with factors and a few have almost none. The first question is how you find out without testing every possibility.
What You'll Explore
4 lessons.
- Divisibility Rules
You can tell at a glance that 4,596 is even. Can you tell as quickly whether it splits into three equal groups with nothing left over? This lesson looks at what the digits of a number reveal about the divisions that come out exactly, and why such quick tests are possible at all.
- Primes and Composites
Most numbers can be split into equal groups in more than one way. Thirteen refuses: one row of thirteen is the only arrangement there is. This lesson sorts every whole number by that difference, asks which side 1 belongs on, and looks at how far you must test before you can be sure.
- Prime Factorization
Break 60 apart one step at a time and you can start anywhere: six times ten, or four times fifteen. Two people doing that will not take the same route. Whether they end up in the same place is the question this lesson settles, along with what those final pieces say about the number.
- GCF and LCM
Two buses leave the same stop on different timetables. When do they next leave together, and how is that anything like finding the largest equal share you can cut from two different piles? These questions seem unrelated. This lesson traces both back to what a pair of numbers has in common.