Topic outline

  • Outcomes



    In this course you will learn about:

    1. The real number system.
    2. Natural numbers, whole numbers and integers.
    3. The highest common factor.
    4. The lowest common multiple.


  • Introduction to real numbers

    The number system contains real numbers and imaginary (or complex) numbers. Real numbers are all the rational and irrational numbers. When people refer to "numbers" they are usually referring to real numbers. We use the symbol \(\mathbb R\) to show real numbers. 

    Rational numbers can be divided further into integers, whole numbers and natural numbers as shown in the image. [edit: I suggest writing image labels in lower case]

    Rational numbers on the number line.


  • Find the highest common factor

    The factors of a number are the numbers you can multiply together to get the number. 

    Example

    \(24=3\times 8\)

    So, \(3\) is a factor of \(24\) and \(8\) is a factor of \(24\).

    A composite number has more than two factors. \(24\) is a composite number since it has more than two factors.

    \(24=1\times 24; 2\times 12; 3\times 8; 6\times 4\)

    A prime number has only two factors, \(1\) and itself. For example, \(17=1\times 17\), the only factors of \(17\) are \(1\) and \(17\).

    Highest common factor (HCF)

    The highest common factor (HCF) (also called the greatest common factor) is the highest common number that divides into two or more numbers. 

    Factors of \(24\) are {\(1; 2; 3; 4; 6; 8; 12; 24\)}

    Factors of \(16\) are {\(1; 2; 4; 8; 16\)}

    The intersection of the two sets of factors is {\(1; 2; 4; 8\)} but the highest number in that intersection is \(8\). Therefore, \(8\) is the HCF of \(16\) and \(24\) .

    You will use HCFs when you factorise so it is a very important concept to fully understand. Watch the next video to gain a deeper understanding of finding the HCF.

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  • Find the lowest common multiple

    A multiple or product is the result of multiplying numbers together. For example, \(8\times3\=24) so \(24\) is a multiple of \(8\) and \(3\). There are infinite multiples of any given number. [edit: the notation for the example is not pulling through correctly]

    Lowest common multiple (LCM)

    The lowest common multiple (LCM) is the smallest number that is a multiple of two or more numbers. 

    Multiples of \(3\) are {\(3; 6; 9; 12; 15; 18; 24; ...\)}

    Multiples of \(8\) are {\(8; 16; 24 ; 32; 40; 48; 56; ...\)}

    \(24\) is the lowest common number to both \(3\) and \(8\) so it is called the LCM of \(3\) and \(8\).

    You use LCMs when you add fractions and need to find the lowest common denominator so it is an important concept to master. Watch the next video for a detailed explanation of finding the LCM.

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