Learning Objectives
- Understand factors and multiples of a number
- Find all factors of a given number
- List multiples of a number
- Identify prime and composite numbers
Key Concepts
What are Factors?
A factor is a number that divides another number exactly, with no remainder. The factors of 12 are: 1, 2, 3, 4, 6, and 12, because all of these divide 12 evenly. Every number has at least two factors: 1 and itself. To find factors, check which numbers divide the given number exactly.
What are Multiples?
A multiple is the result you get when you multiply a number by 1, 2, 3, 4, and so on. The multiples of 5 are: 5, 10, 15, 20, 25, 30... and they go on forever! Multiples of 2 are all even numbers: 2, 4, 6, 8, 10... Multiples of 10 always end in 0: 10, 20, 30, 40...
Factors and Multiples are Related
If 3 is a factor of 15, then 15 is a multiple of 3. They always go together! 4 x 5 = 20, so 4 and 5 are factors of 20, and 20 is a multiple of both 4 and 5. This connection helps you solve many problems quickly.
Prime and Composite Numbers
A prime number has exactly 2 factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13. A composite number has more than 2 factors. Examples: 4, 6, 8, 9, 10, 12. The number 1 is neither prime nor composite (it has only 1 factor). The number 2 is the only even prime number!
Important Terms
- Factor: A number that divides another number exactly with no remainder
- Multiple: The result of multiplying a number by a whole number
- Prime Number: A number with exactly two factors (1 and itself)
- Composite Number: A number with more than two factors
- Common Factor: A factor that two or more numbers share
- Common Multiple: A multiple that two or more numbers share
Quick Revision
- Factors divide a number exactly; multiples are products of a number
- Every number's factors include 1 and itself
- Multiples go on forever: 3, 6, 9, 12, 15...
- If A is a factor of B, then B is a multiple of A
- Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23...
- 1 is neither prime nor composite