Saturday, November 29, 2014

Factors and Multiples

All numbers appear in the Ones times table.

All numbers appear only in their own times table and the Ones times table.

Some numbers appear in more times tables than their own and the Ones times table.

For example consider the numbers Seven and Twelve.

Take seven apples and put them in boxes. We can put all seven apples in one box or one apple in seven boxes.


Now take twelve apples and put them in boxes. We can;

Put all twelve apples on one box

Put six apples in two boxes

Put four apples in three boxes

Put three apples in four boxes

Put two apples in six boxes

Put one apple in twelve boxes

In the game of maths Twelve can be arranged in a variety of equal rows whereas there is only one row arrangement for Seven, ignoring any rotations of the board.

Besides one row of counters Twelve can also be arranged as or whereas Seven can only be arranged in rows as or in columns as on rotation .

A number with only one row arrangement is called a Prime number.

  1. One is not a prime number because
  2. One is what is being counted and
         rotated is the same as

More on prime numbers later.

Card hands that give Twelve

Twelve is in the multiplication tables of One, Two, Three, Four, Six and Twelve. We say Twelve is a multiple of One, Two, Three, Four, Six and Twelve.

One, Two, Three, Four, Six and Twelve are called factors of Twelve.

We sometimes say Three times Four makes Twelve, things are made in a factory from the Latin factor meaning doer or maker and Three and Four are together key factors (doers) in making Twelve.

The cards above show that if you know one factor of a number then there is another factor, its soul mate as it were, which multiplied by the first factor makes the number. Factors always occur in pairs.

For Seven the only pair is One and Seven.

For Twelve the pairs are: One and Twelve; Two and Six; Three and Four.


                 4 and 3 are factors of 12                            12 is  a multiple of 4 and 3

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