Appendix A

worked examples
1 Find the highest common factor 2 Find the lowest common multiple
(HCF) of 102 and 153. (LCM) of 15 and 9.
Number Factors Number Multiples
102 1, 102, 2, 51 , 3, 34, 6, 17. 15 15, 30, 45 , 60, 75, 90, . . .
153 1, 153, 3, 51 , 9, 17. 9 9, 18, 27, 36, 45 , 54, . . .
The common factors are red.
The highest common factor is 51.
There would be other common multiples
but the lowest common multiple can be
seen in the table to be 45.
A:02F Prime and Composite Numbers
• A prime number is a counting number that has exactly two factors, itself and 1.
7 has only two factors, 7 and 1, so 7 is a prime number.
• A composite number has more than two factors.
25 has three factors, 25, 1 and 5, so 25 is a composite number.
• The number 1 has only one factor, 1, so it is neither prime nor composite.
Use a factor tree to write 252 as a product of prime numbers.
252
worked examples
4
63
2 2 3 21
252 = 2 × 2 × 3 × 3 × 7
= 2 2 × 3 2 × 7
2
2
3
3
7
APPENDIX A 7