In mathematics, the factors of a number are the numbers that can be multiplied together to produce that number. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12.
In this article, we will discuss the factors of 30 and how to find them. We will also explore some methods that can be used to determine whether or not two numbers are Factors of 30. Let’s get started!
What are Factors?
Factors are the numbers that can be multiplied together to produce a given number.
For example 2 x 3 = 6 so 2 and 3 are called factors of 6.
What are the Factors of 30?
The factors of 18 are 1, 2, 3, 5, 6, 10, 15, 30.
30 can be divided by these factors and the answer is a whole number.
The process of finding Factors is called factorization. Factorization can be done with or without a calculator, but it is usually easier with one.
To find the Factors of 30 using a calculator, simply enter 30 divided by each of the numbers from one to 30.
If the answer is a whole number, then that number is a Factor of 30. For example, 30 divided by 15 is two so 15 is a Factor of 30. However, if the answer is not a whole number, then that number is not a Factor of 30.
Factor pairs of 30
Because we may multiply two numbers together to get 30, I prefer to consider things in pairs.
1 x 30 = 30
2 x 15 = 30
3 x 10 = 30
5 x 6 = 30
I like to draw factor rainbows to find factor pairs.
Start with 1 and 30.
Then 2 and 15.
Use the divisibility tests to keep going testing 3, then 4 etc.
When you get to 5 & 6 there are no whole numbers between them so then you know you’ve found all the factors.
Prime Factors
Depending how many factors a number has determines if it is a prime number or a composite number.
A prime number has exactly 2 factors. 1 and itself.
For example 5 can only be divided by 1 and 5. It has exactly 2 factors so 5 is a prime number.
A composite number has more than 2 factors.
For example 1 x 6 = 6 and also 2 x 3 = 6 so the factors of 6 are 1, 2, 3 & 6.
Since this is more than 2 factors, 6 is a composite number.
Prime factors are factors of a number that are also prime numbers.
Prime factorization of 30
Draw a factor tree to find the prime factors of 30.
I have circled the prime numbers in red.
So the prime factorization of 30 is
30 = 2 x 3 x 5
Negative factors of 30
The negative factors of 30 are simply -1, -2, -3, -5, -6, -10, -15 & -30.
Both factors need to be negative (or both positive) so that when multiplied the answer is positive 30.
For example -2 x -15 = 30
Final Thoughts on the Factors of 30
Whilst memorizing the factors of 30 is not important, once you master your times tables and multiplication strategies you will be able to find not only the factors of 30 but most numbers. So learning how to find the factors of a number is more important than memorizing them.
Factorizing is an essential math skill for future math topics such as algebra so it is important to understand it now. Practice, practice, practice until you are confident and a factorizing master.
