Finding the factors of a number can be a daunting task, but it doesn’t have to be!
In this article, I show you several different methods for finding the factors of 96. We will start with factor pairs and move onto factor rainbows, prime factorization and more.
By the end of this post, you will know how to find the factors of any number!
What are the Factors of 96?
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 & 96.
Factor Pairs
The factor pairs of 96 are 2 whole numbers that are multiplied together to give an answer of 96.
They are:
1 x 96 = 96
2 x 48 = 96
3 x 32 = 96
4 x 24 = 96
6 x 16 = 96
8 x 12 = 96
So there are 6 factor pairs of 96.
How to find factor pairs of 96
You can use a calculator and the inverse relationship between multiplication and division to find any factors.
If you know a x b = c, then c divided by a equals b.
For example 2 x 3 = 6, so 6 divided by 2 equals 3.
Applying this to 96, we can use our calculator to enter:
96 divided by 2 and the answer is 48.
This means 2 x 48 = 96, so 2 and 48 are factor pairs of 96
You can work methodically by dividing 96 by every whole number starting at 1 to find the factor pairs. The answer needs to be a whole number because factors are whole numbers.
After I got to 8 x 12 = 96 I tested the whole numbers in between 8 and 12 and since 9, 10 & 11 are not factors of 96 I know that I’ve now found all the factor pairs.
Factor Rainbows
Factor rainbows are a colorful way to find the factor pairs of any number.
You can use a calculator or the divisibility tests to determine if a number is a factor of 96 starting with 1.
Once you get a factor pair that doesn’t have any more whole numbers between them or none of the numbers between them are factors, then you know you have found all the factor pairs.
Prime Factors of 96
To find the prime factorization of 96 draw a factor tree.
There are multiple ways to draw a factor tree.
Here is one possible factor tree for 96.
Here is another factor tree for 96:
The prime factors of 96 are 2 & 3.
Prime Factorization of 96
We can use the prime factors to write 96 as a product of its prime factors like this:
96 = 2 x 2 x 2 x 2 x 2 x 3
In index notation it looks like this:
Negative Factors of 96
The factors of 96 are -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48 & -96.
To get a product with a value of +120, the two factors must both be negative (or both positive).
Final thoughts on the Factors of 96
To summarise there are many ways to find the factors of a number. You can use a calculator, divisibility rules, factor pairs, factor rainbows or prime factors. Keep practicing the different methods so you are confident to find the factors of any number.
