Introduction to Number Systems

This course is about the counting numbers and how they are built. It begins with counting itself. It ends with the highest common factor and the least common multiple. It is meant for a student who already knows the times tables. Every rule is stated plainly, and then the reason behind it is shown.

The lessons build on one another in order. The first names the natural numbers and the whole numbers, then sorts every whole number into even or odd. The next reads a single multiplication two ways, as multiples and as factors. A lesson then puts letters in place of numbers and writes repeated multiplying as a power. Two lessons of divisibility rules follow, first for $2$, $3$, $4$ and $5$, then for $6$ up to $11$. Counting factors sorts numbers into prime and composite, and names perfect numbers, coprimes and twin primes. Prime factorisation then takes a composite number apart into primes. The last three lessons find the H.C.F, then the L.C.M, then the link between the two.

By the end you will be able to:

• say whether a whole number is even or odd from its last digit;
• write out the multiples of a number, and list every one of its factors in pairs;
• write a number such as $1024$ as $2^{10}$;
• test a number for division by $2$ up to $11$ without doing the division;
• count a number's factors to say whether it is prime or composite;
• write a composite number as a product of primes, and shorten it with indices;
• find the H.C.F and the L.C.M three ways each, and check that the answers agree;
• find the H.C.F and the L.C.M of fractions such as $\displaystyle \frac{3}{4}$ and $\displaystyle \frac{9}{10}$.

The last lesson works through problems set as stories, where you must decide for yourself whether the question is asking for the H.C.F or the L.C.M.