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Maths: Grade 6
Numbers, Operations & Relationships: Factors
FACTORS
A factor is a whole number that can be divided exactly into another whole number
without a remainder. 1 and the number itself are always factors. Factors come in pairs.
Example
Factors of 12.
We write them like this:
To check that you have all the factors of 12, use lines with arrows and pair the numbers
from left to right. Each factor must have a partner that it can be multiplied with to give
the original number.
So the factor pairs of 12 are 1 and 12, 2 and 6 and 3 and 4, i.e:
1 x 12 = 12
3 x 4 = 12
2 x 6 = 12
A partner may also be the same factor.
Example
Factors of 16:
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Maths: Grade 6
Numbers, Operations & Relationships: Factors
In the above example, the factor pairs are 1 and 16, 2 and 8 and 4² is 4 and 4.
Remember that the factors of a number are always written in ascending order.
Prime Numbers
A number is a prime number if it only has 2 factors and those numbers must be 1 and the
number itself. 1 is not a prime number because it only has 1 factor. 2 is the only even
number that is a prime number.
Examples of Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19, 23 etc.
All of the above are prime numbers because 1 and the number itself are factors.
Composite Numbers
Numbers that have more than 2 factors are called composite numbers. These numbers
can be divided evenly by another number, except 1 and itself.
Examples
4, 6, 8, 10, 12, 14, 16, 18, 20, etc.
These are just a few. There are many other natural numbers/whole numbers that are
composite.
Natural Numbers
These are our counting numbers and go on to infinity.
Example
1, 2, 3, 4, 5, 6, 7, 8, 9, etc.
Whole Numbers
These include zero plus our counting numbers and go on to infinity.
Example
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, etc.
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Maths: Grade 6
Numbers, Operations & Relationships: Factors
Rational Numbers
A number that can be written in the form of a fraction where the denominator is not equal
to zero, is a rational number.
Example
!
6=!
0,01 =
!
!""
!
0,5 = !
Factor Trees
Every composite number can be written as a product of its prime factors. We can use a
factor tree to find the prime factors of a number. We carry on breaking down the
numbers into pairs until all the numbers are prime numbers.
Example
The Prime Factors of 36:
Firstly the factors of 36 are:
You can use any of the pairs, but we will use factor pairs 12 and 3 and 18 and 2 to find
the prime factors of 36 in our factor tree.
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Maths: Grade 6
Numbers, Operations & Relationships: Factors
First you write 36 as the original number, then the pairs are added as 'leaves' below the
original number. Circle the leaves that are prime numbers and break down all the leaves
until they are prime.
So 36 = 3 x 2 x 2 x 3
OR
2
2
2
2
=3 x2 =2 x3
36 = 2 x 2 x 3 x 3
Now 36 has been written as a product of its prime factors.
In the factor trees above, the leaves with the prime numbers have been circled and all the
numbers have been broken down until they are prime.
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