Numbers, Factors and Primes
Build precise number language before formal algebra and proof.
Lesson focus
Build precise number language before formal algebra and proof.
Read the worked example, then use the practice and quiz to check your understanding.
Factors and prime factorisation
A factor divides a number exactly. A prime number is greater than 1 and has exactly two positive factors: 1 and itself.
Example: $84=2^2[[cdot]]3[[cdot]]7$.
Writing general integers
Every even integer can be written as $2k$. Every odd integer can be written as $2k+1$, where $k$ is an integer. This is useful because it proves a statement for any even or odd number, not just a few examples.
Example: $(2a+1)+(2b+1)=2(a+b+1)$, so the sum of two odd integers is even.
Before you leave
Write a complete mathematical sentence, not only a final number. Check whether your answer matches the condition in the question.
Practice Problems
Attempt each question before opening its answer.
Practice 1
Find the HCF and LCM of 36 and 48.
Show answer
$36=2^2[[cdot]]3^2$ and $48=2^4[[cdot]]3$.
HCF $=12$; LCM $=144$.
Practice 2
Write an integer that leaves remainder 3 when divided by 7.
Show answer
$7k+3$, where $k$ is an integer.
Interactive Quiz
Check one key idea before you move on.