Factor Family
When asked to find all the factors of a number, I like
to think of them as members of a family.
The HEAD of the family is the number that you have
to find factors of.
Some rules apply –
1) There can only be ONE HEAD of the family;
2) Family members (factors) come in pairs;
3) Sometimes there are special pairs who are
identical twins.
Here is an example:
Find all the factors of 40:
40 – (head of the family)
40
1
40
40 2 20
40
4 10
40
5
8
What does factors mean?
How did I work out the factors of 40?
The factors of 40 are
1, 2, 4, 5, 8, 10, 20 and 40.
I see
Checking:
40 = 1 x 40
How many 1s go into 40?
40 = 2 x 20
How many 2s go into 40?
40 = 4 x 10
How many 3s go into 40?
40 = 5 x 8
Here is another example:
Find all the factors of 36:
36 – (head of the family)
36
1
36
36 2 18
36
3 12
36
6
6
Are these all the factors of 36?
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36
Some of the factors of 36 are very special.
Can you spot them?
Can you explain why they are special?
2 is a prime number;
3 is a prime number;
6 is a twin so it’s written
once on the list.
Is there something that you must remember to
help you find the factors of any number?
Exercise 1: Match the factors to their number.
You can re-use any of the factors.
Number
Factors
14
1
8
4
16
9
3
50
23
2
25
5
27
50
Are some
missing?
Exercise 2:
Find all the factors of
1. 15
5. 42
2. 18
6. 55
3. 25
7. 75
4. 28
8. 89
Are any of them special and Why?
Exercise 3:
Each number has something in common besides the
number 1 as a factor. What is it?
For example:
The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40
Hint: Every number has
this ‘type of a number’ as
a factor.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36
The factors of 15 are 1, 3, 5 and 15
The factors of 11 are 1 and 11
Challenge:
Can you create a number equation with this ‘type of a number’ to the number
(head of the family) whose factors you are trying to find.
Would your number equation work if this ‘type of a number’ is the same as the
number (head of the family) whose factors you are trying to find?
The skills used to find factors and know them is useful in other areas of
mathematics, like – simplifying fractions, ratio and proportion. It helps to
find solutions faster.
In daily life you can use the same skill to help with money. Bank clerks
use them all the time.
This is a coin bag used by
banks to store coins.
Exercise 4:
How many £1 coins can you place in this bag?
How many £2 coins can you place in this bag?
How many 50p coins can you place in this bag?
How many 20p coins can you place in this bag?
How many 10p coins can you place in this bag?
How many 5p coins can you place in this bag?
How many 2p coins can you place in this bag?
How many 1p coins can you place in this bag?