The earliest evidence of math comes from ancient Mesopotamia.
We also have proof of complex math equations written on papyrus by Ancient Egyptians.
Clearly, mathematics has been an important part of life for quite some time!
And one critical math methodology is factors.
In this article, we’re going to explore the factors of 18.
Let’s dive in!
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Factors: Explaining the Terminology
A factor is a numeral that divides into another numeral perfectly – without any decimals or remainder left over.
With the definition behind us, let’s answer the question at the center of this article:
“What are the factors of 18?”
If we were to list the factors of 18, the list would look like this:
1, 2, 3, 6, 9, and 18.
But that’s just the beginning.
Next, this set of numbers gets broken down into two smaller sets: factor pairs and prime factors of 18.
What Are the Factor Pairs of 18?
Now that you know all the factors of 18, it’s time to dive a little deeper. First up, we’ll explore the factor pairs of 18.
A factor pair is a group of two numbers that can multiply together to provide the original number (in this case, 18).
Of the six factors of 18, we get three pairs:
1 and 18
2 and 9
3 and 6
Take a closer look at these pairs. Notice something about them?
That’s right…they all equal 18 when multiplied together.
The equations look like this:
1 x 18 = 18
2 x 9 = 18
3 x 6 = 18
There are a few things to note about factor pairs. The first is that square numbers always have odd sets of pairs.
Also, negative integers aren’t helpful in this instance – you’ll just get the exact same numbers, but negative!
Though, of course, if you want to include negative numbers, you’ll get double the number of factors.
Having a hard time with these equations? The internet’s here to help!
Try out this handy dandy online factor pairs calculator.
What Are the Prime Factors of 18?
The other types of factors you need to know about are prime factors.
They consist of prime numbers (positive integers that can be evening divided by 1 and themselves) multiplied together to give the answer of 18.
To find the prime factors of 18, you need to undertake a process called prime factorization.
In the case of the prime factorization of 18, you divide this number by the smallest prime number possible.
Then, you need to divide that answer by the smallest prime number possible. Repeat until you get down to 1.
These can be represented as written equations:
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 3
If you group all of the answers to those equations together, you can see that the prime factors of 18 are:
2, 3, and 3
18, we’ve discovered, has just three prime factors in total!
Still confused? Don’t want to do the math yourself? Use this prime factor calculator!
Uncovering the Factors of 18
So, there you have it: there are six factors of 18 to know about!
Are you looking for more math theory? Check out the other articles on our site.
We have articles on the factors of many numbers and other helpful math equations to explore.
For related info, check out this post about how many hours are in a year.