A fraction is a number that is used to represent a whole number that has been divided into equal parts. For example, if we divide a cake into eight equal parts and take one piece, this would mean that 1/8 of the cake is gone and 7/8 is left.
What is a Factor in Maths?
A factor in maths is one of two or more numbers that divides a given number without a remainder.
In other words, a factor is a number that divides another number evenly.
For example, 5 X 2 = 10, so 5 and 2 are factors of 10.
Any given number can have many factors.
Factors are found not just in numerical sums but also in algebraic equations.
Factoring is the opposite of expanding.
How to Calculate Factors
One of the easiest ways to calculate factors is to use a factor tree.
This simple root-and-branch approach determines which can be multiplied to reach a particular number.
The main aim of this method is to find prime factors: numbers that cannot be factored down anymore.
A factor tree for the number 24, for example, would look like this:
24
4 X 6
2 X 2 X 2 X 3
Therefore, the factor of 24 is 2 X 2 X 2 X 3.
Every number that is not one can be expressed as the sum of its prime factors.
Factor Pairs
What are factor pairs?
Factor pairs are about whichever possible combination of two numbers that act as factors of a multiple, which will give a known product when multiplied together.
A factor pair is two numbers that multiply together to yield a common multiple.
Example:
Ten × 2 = 20, with 10 and 2 acting as factor pairs, with a product of 20 and factors of 10 and 2.
For the multiple of 20, 10 and 2 aren’t the only factor pairs.
5 and 4 are factor pairs of the multiple of 20, as are the numbers 1 and 24.
Different Types of Factor
Prime Factor
What is a prime factor in maths? Most numbers have an even number of factors, while a prime number has only two factors – the prime number itself and the number 1- and, therefore, only a one-factor pair.
This means a prime factor is simply a factor that is a prime number.
In other words, it is a number greater than one but one which cannot be divided precisely except by itself or by 1.
This fantastic video will quickly explain how to calculate the prime factor in a sum.
Common Factor
When working out the factors of two or more numbers, you will often find that their elements overlap.
We call these overlapping numbers ‘common factors’.
For example, using the model of 18 and 24, common factors which will multiply into both include 1, 2, 3, and 6.
Highest Common Factor
As you may have guessed, the highest common factor in a sum is the highest number of the common elements you have identified.
What is a factor in Algebra?
In algebraic equations, factors are expressed differently from the sums we have seen before.
Here, factoring, or factorizing, is done by finding an expression by multiplying simpler terms together.
For example, if you are asked to factor 2x+4:
2x is 2 lots of x.
4 is two lots of 2.
So, to factorize the sum, we combine the two:
2x+4=2(x+2).
The opposite of factoring is expanding.
Expanding a bracket means multiplying each term by the expression outside the frame.
You’ll see it is much like factoring, just the other way around. Knowing how to expand will help you to remember how to factor.
We can expand the answer we got above by following this process.
For example, with the expression 2(x+2), we multiply both x and two by the number outside the bracket. In this case, that’s the number 2. So:
2(x+2) = 2 X x + 2 X 2 = 2x+4
Both expanding and factorizing make use of the skills of simplifying algebra.
What is the Difference Between a Factor and a Multiple?
Although factors and multiples are directly linked, they are two different things.
Where factors refer to the numbers that can be multiplied to reach a number, a multiple is a result after the elements are multiplied.
So, multiples result from multiplication, whereas factors are the numbers that create the sum.
