Number Patterns: Dot Representation, Even and Odd Numbers, Factors and Multiples
Number patterns reveal structure in quantities. Dots can form geometric arrangements, while divisibility ideas lead to factors, multiples, the HCF and the LCM.
Dot patterns
A square number is a product of two equal factors, such as 9 = 3 × 3. Triangular numbers can be formed by adding successive counting numbers: 1, 3, 6, 10, 15, … . Rectangular arrangements show factor pairs.
Even and odd numbers
An even number is exactly divisible by 2 and has last digit 0, 2, 4, 6 or 8. An odd number is not exactly divisible by 2 and has last digit 1, 3, 5, 7 or 9.
Factors, multiples, HCF and LCM
A factor divides a number exactly; a multiple is obtained by multiplying a number by a whole number. For 12, the factors are 1, 2, 3, 4, 6 and 12. The HCF is the greatest common factor, while the LCM is the first positive common multiple.
Worked examples and practice
- Factors of 18 are 1, 2, 3, 6, 9 and 18.
- Multiples of 4 are 4, 8, 12, 16, … .
- Using prime factors, HCF(18, 24) = 6 and LCM(18, 24) = 72.
- Draw dot arrangements for 12 and 16. Find the HCF and LCM of 20 and 30.
