# Highest common factor (HCF) Factor pairs Multiples Factorised ```Highest common
factor (HCF)
Factor pairs
Multiples
Factorised
Product of prime
numbers
(or prime
factorisation)
Common factor
Prime number
Composite number
Factors
The factors of a positive integer are the positive
integers which divide exactly into it.
A prime number is a natural number which has exactly
two different factors.
A composite number is a natural number which has
more than two factors.
For example, the only two factors of 3 are 3 and 1, and
of 11 are 11 and 1.
8 is a composite number since it has four factors: 1, 2,
4, and 8.
For example, the factors of 8 and 1, 2, 4, and 8
since 8 &divide; 1 = 8
8&divide;2=4
8&divide;4=2
and
8&divide;8=1
To express a composite number as the product of
prime numbers, we systematically divide the number
by the prime numbers which are its factors.
When we write a number as a product of factors, we
say it is factorised.
A number which is a factor of two or more other
numbers is called a common factor of those numbers.
10 may be factorised as a product of two factors in two
ways: 1 x 10 or 2 x 5.
For example, 5 is a common factor of 25 and 35.
We can find the highest common factor (HCF) of two
or more natural numbers by first expressing then as
the product of prime factors.
The multiples of any whole number have the number
as a factor. They are obtained by multiplying the
numbers by 1, then 2, then 3, then 4, and so on.
All positive integers can be split into factor pairs.
For example:
8 = 8 x 1 or 2 x 4
The multiples of 10 are
1 x 10, 2 x 10, 3 x 10, 4 x 10, 5 x 10, …
or
10, 20, 30, 40, 50, …
Likewise, the multiples of 15 are 15, 30, 45, 60, 75, …
Product
Consecutive
numbers
Exponential notation
Odd number
The rules for order of
operations to evaluate
(or simplify) an
expression
Consecutive even
&amp;
consecutive odd
numbers
Common multiple
Lowest common
multiple (LCM)
Even number
The number 30 is a multiple of both 10 and 15, so we
say 30 is a common multiple of 10 and 15.
The lowest common multiple (LCM) of two or more
numbers is the smallest number which is a multiple of
each of those numbers.
A whole number is even if it has a 2 as a factor and
thus is divisible by 2.



A whole number is odd if it is not divisible by 2.
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Perform operations within Brackets first.
Calculate any part involving Exponents.
Starting from the left, perform all Divisions and
Multiplications as you come to them.
Finally, working from the left, perform all
An amount obtained as a result of multiplying
numbers.
Consecutive numbers are numbers in counting order,
without gaps.
One example of four consecutive numbers is
6, 7, 8, 9.
Consecutive even numbers are even numbers that
come in a row. Consecutive odd numbers are odd
numbers that come in a row.
One example of three consecutive even numbers
is 6, 8, 10.
One example of three consecutive odd numbers
is 13, 15, 17.
A convenient way to write a product of identical
factors is to use exponential or index notation.
For example, 2 x 2 x 2 x 2 x 3 x 3 x 3
can be written in exponential notation
as 24 x 33(four factors of 2 and three factors of 3).
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