Special numbers
Working with special numbers
Some numbers are special because of how they behave. In this unit you work with odd and even numbers, factors and multiples, and square numbers.
Odd and even numbers
Even numbers can be shared into two equal groups. They end in 0, 2, 4, 6 or 8. Even numbers: 0, 2, 4, 6, 8, 10, … Odd numbers cannot be shared into two equal whole groups. They end in 1, 3, 5, 7 or 9. Odd numbers: 1, 3, 5, 7, 9, 11, …
Factors and multiples
A factor divides a number exactly, with nothing left over. Factors come in pairs. The factors of 12 are 1, 2, 3, 4, 6 and 12. A multiple is what you get when you count in steps of a number. The multiples of 5 are 5, 10, 15, 20, 25, … Every number with a factor of 6 also has factors of 2 and 3, because 6 = 2 × 3.
Square numbers
A square number is made by multiplying a whole number by itself. You can arrange that many dots into a square. 1 × 1 = 1, 2 × 2 = 4, 3 × 3 = 9, 4 × 4 = 16, 5 × 5 = 25. So the square numbers are 1, 4, 9, 16, 25, 36, …
Worked examples
Finding a square number
- Find the 4th square number.
- Multiply the position by itself: 4 × 4.
Answer: 16.
Finding the factors of a number
- Find every number that divides 12 exactly.
- List the pairs: 1 × 12, 2 × 6, 3 × 4.
Answer: 1, 2, 3, 4, 6 and 12.
Finding a multiple
- Find the 3rd multiple of 5.
- Count on in fives: 5, 10, 15.
Answer: 15.
Where you see this in real life
- Many flowers have 3 or 5 petals, which are odd numbers.
- Arranging tiles into a perfect square uses square numbers.
- Sharing sweets into equal groups uses factors.
Key words
- Even number
- A number that ends in 0, 2, 4, 6 or 8 and can be split into two equal groups.
- Odd number
- A number that ends in 1, 3, 5, 7 or 9.
- Factor
- A whole number that divides another number exactly.
- Multiple
- The result of multiplying a number by a whole number, like 5, 10, 15 for 5.
- Square number
- A number made by multiplying a whole number by itself, such as 16 = 4 × 4.