Factorials
The factorial of a number which is positive in nature is a multiplication sum.
How to calculate factorials involves multiplying the relevant positive number with a list of descending smaller numbers down to the number 1.
The symbol used to represent a factorial is an exclamation mark. !
Thus writing down four factorial would be 4!.
With it representing the following:
4! = 4 × 3 × 2 × 1 = 24
So in general, the factorial of a positive number r is:
r! = r × ( r − 1 ) × ( r − 2 ) × ……… × 1
How to Calculate Factorials, 0!
A special case to mention when thinking about how to calculate factorials, is zero factorial, 0!.As unexpectedly, the value of zero factorial is 1.
To get a picture of why this is the case, we can rewrite the general factorial rule above slightly differently.
r! = r × ( r − 1 )!
Now it’s the case that 1! = 1.
So we’d have: 1! = 1 × ( 1 − 1 )!.
Which is: 1! = 1 × ( 0 )!.
Meaning that 0! has to be equal to one for this to be true.
Multiple of a Number
In Math, a multiple of a number is the result of multiplying a given number by an integer.
We can look at the number 6 as an example.
6 × 2 = 12 , 6 × 1 = 6 , 6 × 3 = 18
6 × -1 = -6 , 6 × -4 = -24
So 12 , 6 , 18 , -6 and -24 are all multiples of the number 6.
They are all the result of multiplying 6 by an integer.
It’s the case that fractions and irrational numbers can have multiples also.
\bf{\frac{1}{4}} × 1 = \bf{\frac{1}{4}} , \bf{\frac{1}{4}} × 3 = \bf{\frac{3}{4}}
are sums that give multiples of \bf{\frac{1}{4}}.
An irrational number such as π, will have multiples of the form:
2π 5π etc.
Factor of a Number
A factor of a certain number, is another number that can divide the certain number evenly, with no remainder.
This also includes the certain number itself.
Take the number 16 for example.
The numbers 1 , 2 , 4 , 8 , 16 are factors of 16.
( 16 ÷ 1 = 16 , 16 ÷ 2 = 8 , 16 ÷ 4 = 4 , 16 ÷ 8 = 2 , 16 ÷ 16 = 1 )
Factors and Factor Pairs:
A ‘factor pair’ is two factors of a given number, that multiply together to result in that given number.The factor pairs of 16 are:
1 and 16 , 2 and 8.
=> ( 1 × 16 = 16 , 2 × 8 = 16 )
Similarly, the factor pairs of 12 are:
1 and 12 , 2 and 6 , 3 and 4.