Chapter 05
Factors and multiples
Every whole number can be built by multiplying smaller whole numbers together. The pieces it is built from are its factors, and the numbers it helps build are its multiples.
Both ideas come back constantly: simplifying a fraction is finding a factor the top and bottom share, and adding two fractions is finding a multiple they both reach.
Factors and multiples
Factors are numbers that multiply together to make another number. Multiples are what you get when you multiply a number by whole numbers.
- 3 × 4 = 12, so 3 and 4 are both factors of 12.
- All the factors of 12 are 1, 2, 3, 4, 6 and 12.
- The multiples of 4 are 4, 8, 12, 16, 20, 24 and so on.
- The greatest common factor is the biggest factor two numbers share.
Greatest common factor of 12 and 18
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
The biggest one in both lists is 6.
Key words
Much of pre-algebra is vocabulary. A question names what it wants in these terms, and the term decides which arithmetic answers it.
- Factor
- A number that divides into another number evenly.
- Multiple
- What you get when you multiply a number by a whole number.
Where this leads
- Fractions, decimals and percents
- Simplifying a fraction is a shared factor divided out of the top and the bottom.