 11 and 33 are factors of 66.

# Level 3-4 Algebra - Factors

If you are studying KS3 Maths then you should be familiar with factors. Ever since you learned your times tables you've been dealing with factors. And now you have moved on to algebra you'll find factors very useful.

The factors of a number are the numbers that divide exactly into it. Basically, if a number appears in any of the times tables then the number of the times table is a factor of it. For example, 64 appears in the 1, 2, 4, 8, 16, 32 and 64 times tables so those numbers are all factors of 64.

You can divide any number into any other number but it is a factor only if the result is a whole number. So, one way to work out if a number is a factor of another is to divide the larger number by the smaller. If the answer is a whole number then it is a factor - if the answer is not a whole number then it is not a factor.

That all sounds quite simple doesn't it? To see if you've found your way around factors, have a go at this quiz. Take your time and read every question carefully!

1.
Which of these is not a factor of 60?
10
15
20
25
The 25 times table goes from 50 to 75. 60 is not in it
2.
Which of these is a factor of 66?
3
4
8
12
22 x 3 = 66
3.
Which of these is a factor of 70?
9
10
11
12
7 x 10 = 70
4.
Which of the following is a factor pair of 32?
2 and 14
2 and 16
2 and 18
2 and 20
An easy one this. 2 x 16 = 32
5.
Is 4 a factor of 21?
Yes
No
Seldom
Often
If you divide 4 into 21 the answer is 5.25. Because the answer is NOT a whole number, 4 is NOT a factor of 21
6.
Which of these sets of numbers are all factors of 80?
2, 4, 8, 16
2, 4, 8, 12
4, 8, 16, 18
2, 4, 14, 20
In all the incorrect answers there is a number that will not divide into 80 and give a whole number as the result
7.
Which of these sets of numbers are not all factors of 100?
2, 4, 10
5, 10, 20
2, 20, 50
20, 40, 50
In the correct answer, 40 cannot be divided into 100 and give a whole number as the result
8.
A number which divides exactly into two other numbers is what sort of factor of those numbers?
Cheap
Expensive
Common
Frequent
The two numbers have that factor in common
9.
Which of these is not a factor of 80?
2
3
4
5
26 x 3 = 78 and 27 x 3 = 81. 80 cannot be divided by 3 to a whole number
10.
Which of these is a factor of 33?
7
9
11
13
11 is the only one that can be divided into 33 and produce a whole number
You can find more about this topic by visiting BBC Bitesize - Prime numbers, factors and multiples

Author:  Frank Evans 