Finding the prime factors of a number is a process that can be done with pencil and paper, or with a calculator. In this article, I will show you how to find the prime factors of 56 both ways.
As a high school math teacher since 2007, finding factors is an essential skill for many topics including fractions, ratios & algebra.
Let me show you how to find the prime factors of 56 so that you can then apply these skills to other numbers.
What is the prime factorization of 56?
The prime factors of 56 are 2 and 7.
So we can say 56 = 2 x 2 x 2 x 7
The prime factorization of 56 can be found using a factor tree or calculator.
How to find the prime factors of 56 using a factor tree
First, let’s take a look at how to find the prime factors of 56 with pencil and paper.
To find the prime factorization of 56 using pencil and paper, we first draw a factor tree. The numbers at the bottom of the tree are the prime factors of 56.
There are many ways to draw a factor tree for 56. Here is one of them.
The prime factors of 56 are 2 and 7.
How to find the factors of 56 using a calculator.
Now let’s take a look at how to find the prime factors of 56 with a calculator.
To find the prime factors of 56 with a calculator, we need to divide 56 by every whole number starting with 1. If the answer is a whole number then this is a factor pair with the dividend.
i.e 56 divided by 1 is 56, so the factor pair is 1 and 56
56 divided by 2 is 28, so the factor pair is 2 and 28.
56 divided by 3 is not a whole number, so 3 is not a factor of 56.
56 divided by 4 is 14, so the factor pair is 4 and 14.
56 divided by 5 is not a whole number, so 5 is not a factor of 56.
56 divided by 6 is not a whole number, so 6 is not a factor of 56.
56 divided by 7 is 8, so the factor pair is 7 and 8.
There are no more whole numbers between 7 & 8 so now we know we have found all the factors of 56.
What are the factors of 56?
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56.
What are the factors pairs of 56?
The factor pairs for 56 are 1 and 56; 2 and 28; 4 and 14; 7 and 8.
How to use the divisibility tests to find the factors of 56.
Another way to find the factor pairs of 56 is to draw a factor rainbow and use the divisibility tests.
Start with 1 and 56.
Then try the next whole number after 1 which is 2.
56 ends in an even number so that means 56 is divisible by 2. 56 divided by 2 is 28, so the factor pair is 2 and 28.
The next whole number after 2 is 3. But 56 is not divisible by 3 because the sum of the digits 5+6 is 11 and 11 is not divisible by 3.
The next whole number is 4. 56 divided by 4 is 14. The divisibility test for 4 is if the last 2 digits is divisible by 4.
56 is not divisible by 5 since the last digit is not a 0 or 5.
56 is not divisible by 6 since it is not divisible by both 2 & 3.
7 is the next whole number to test. 7 times 8 is 56.
There are no more whole numbers between 7 & 8 so you know you have found all the factor pairs.
What is the product of prime factors of 56?
56 can be written as the product of its prime factors as 56 = 2 x 2 x 2 x 7
We can write this in index notation like this:
What is the greatest prime factor of 56?
7 is the greatest prime factor of 56
Negative factors of 56
The negative factors of 56 are -1, -2, -4, -7, -8, -14, -28, -56.
For the product to be positive 56, both factors must be negative (or both positive).
Final thoughts on the factors of 56.
The next time someone asks you what the factors of 56 are, you’ll be able to tell them without blinking an eye. And if that person is really lucky, maybe you’ll even show them how it’s done.
In the meantime, practice so you can find the factors of any number – it will come in handy for other math topics!
Further factors
Learn more about the factors of other numbers here.
