What are the factors of 24? How do you find factors? And what are factor pairs?
In this lesson, we are going to find out the answers to all these questions!
A factor is simply a number that goes into another number exactly. For example, 10 is a factor of 100 because 100 can be divided by 10.
Once you know how to find factors, you will easily find any numbers factors!
All Factors of 24
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24!
24 has 8 factors in total.
Factor Pairs of 24
Factor pairs are two whole numbers that multiply together to the original number.
A factor pair of 24 is two numbers that multiply together to make 24. You should write factor pairs in brackets.
The factor pairs of 24 are:
As two negative numbers can be multiplied together to make a positive number, the negative factors can also be written down in factor pairs.
The negative factor pairs of 24 are:
Fun Factor Fact!
Each number in a factor pair can be called a factor or a divisor. The sum of all the divisors of 24 is 60:
The proper factors of a number are the divisors other than the number itself, so the sum of the proper factors is 35:
If the proper factors add up to more than the number itself, then it is an abundant number!
24 is an abundant number as the sum of its proper divisors is greater than the number itself.
Prime Factors of 24
A prime number is a number that can’t be divided by anything other than 1 and itself.
For example, 5 cannot be divided by anything other than itself and 1, so it is a prime number.
Prime factors are primes that are also factors.
Let’s remind ourselves of the factors:
There are only two prime numbers in this list:
So 2 and 3 are 24’s prime factors.
How to Find the Factors of 24
To find all of 24’s factors, you must start at 1 and see which numbers go into 24 exactly.
If you divide 24 by a number and the answer is whole, then the number is a factor.
You only need to check for factors between the two numbers in the most recent factor pair you have found. You’ll see this in action in just a moment.
To find the factor pairs of 24, start at 1…
There is no remainder, so 1 and 24 are factors.
2 and 12 form a factor pair: (2,12). Now check for factors between 2 and 12.
So, 3 and 8 are both factors. Now check for factors between 3 and 8.
4 and 6 are both factors. Now check for factors between 4 and 6.
The only number left to check is 5.
When 24 is divided by 5, the result has a remainder, so 5 is not a factor.
All the positive factor pairs of 24 have now been found.
The negative factors can also be written down because when you multiply two negative numbers together, the answer is always positive.
In total, 24 has the factors:
Here are some tricks to easily spot whether a number is a factor:
- All integers have a factor of 1.
- All even numbers have a factor of 2.
- If the sum of a number’s digits is a multiple of 3, it has a factor of 3.
- If the last two digits of a number are 00 or divisible by 4, it has a factor of 4.
- A number with last digit 0 or 5 has a factor of 5
- An even number whose digits have a sum which is a multiple of 3, has a factor of 6.
- 7’s divisibility test is a bit more involved, so we’ll go into in the linked article.
- If the last 3 digits of a number are divisible by 8, it will have a factor of 8.
- If the sum of a number’s digits is 9, then it has a factor of 9.
- If the last digit of a number is 0, it has a factor of 10.
These are so useful in fact, that we made a printable table and worksheet for the divisibility rules from 2 to 15, for you to keep with you. Just click or tap the images below to get them for yourself!
Prime factorization of 24
Prime factorization is a way of writing down the product of all the prime factors.
There are two methods to find the prime factorization of 24.
Method One: Division
The first method involves breaking down 24 by its prime factors until you reach 1.
Starting with the smallest prime factor and working upwards, divide 24 and the results by its prime factors.
If you get a number that isn’t whole, divide by the next smallest prime factor.
Once 1 is reached, all the factors needed to write 24 as a product of prime factors are found.
To find the prime decomposition of 24, we need to find the factors of 24, which are divisible only by themselves, and 1. These are 2 and 3.
Starting with 2, the smallest of 24’s prime factors…
24 ÷ 2=12
This results in a whole number, so you can continue dividing by 2.
6 ÷ 2 = 3
3 ÷ 2 = 1.5
This is not a whole number, so instead, try dividing by the next smallest prime factor 3.
The result has reached 1, so all the prime factors needed to express 24 have been found.
We don’t include 1 in this multiplication, as 1 is not a prime.
Cleaning up the product…
Method Two: Factor Tree
Prime factorization can also be done using a prime factor tree, which some people find a lot easier!
Choose a factor pair and keep dividing it until you reach prime numbers!
Choosing the factor pair with the smallest prime keeps it neat, (2,12) …
As 2 is a prime factor, we can circle it to show this is the end of the branch.
Continue breaking 12 down into its factors…
Break 4 down into its factor pair (2, 2) …
And there you have it! The end of every branch is circled, so the prime factor tree is complete. 24’s prime decomposition is written as the multiplication of the circled factors:
Or, written more simply:
It is cool because you could have started with any factor pair and ended with the same result. Isn’t math amazing?!
a) 81 = 34
b) 75 = 3 × 52
Isn’t 24 Interesting?
24 is the karat number of 100% pure gold.
There are 24 letters in the modern and classical Greek alphabet.
24 elements make up the human body.
There are 24 cycles in the Chinese solar year: their year is split into 24 parts.
To Sum Up (Pun Intended!)
Only a factor divides a number exactly without leaving a remainder.
The factors of 24 are:
24 can be shown as the product of its prime decomposition or as factor pairs.
Factor pairs are easy to find; you need to start at 1 and keep going!
How did you find the challenges? Let us know and ask us any questions you have in the comments below!