What Are the Factors of 24?

By Staff WriterLast Updated May 27, 2020 7:35:11 PM ET
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The factors of 24 are: one, two, three, four, six, eight, 12 and 24. All of these numbers are integers that you can multiply by another integer to get the number 24. There are multiple ways to discover all of the factors of a number.

The Definition of a Factor

A factor is any number that you can evenly divide into another number. For example, if you divide 20 by five, five will go into 20 evenly four times. However, if you divide 20 by 11, 11 will only go into 20 once. It has a remainder of nine. Any number that has a remainder when you divide it into the given number is not a factor.

Finding Factors by Using the Prime Factors

One method that you can use to help you find all the factors of a number is to first start by finding the number’s prime factors. A prime factor is a factor that’s also a prime number. A prime number is a number that’s only divisible by one and itself.

Before you get started, remember that every number is divisible by one and itself. So, you can start by stating that one and 24 are factors of 24. 

With the number 24, two is the smallest prime number that divides evenly into it. You can multiply two by 12 to yield 24. Since two is a prime number, you don’t need to do anything else with it. 

However, you do need to find the rest of the factors for the number 12 to discover more factors. The number 12 is divisible by one, 12, one, six, three and four. You know that 24 is divisible by 12, which means it’s also divisible by 12’s factors. Your total list of factors for 24 should now read one, two, three, four, six, 12, and 24.

The number 24 has another prime factor because three multiplied by eight also yields 24. Again, since three is a prime number, it has no factors other than one. However, the number eight has the following factors: one, eight, two and four. This means that eight needs to be added to the list of factors for 24. That list now reads: one, two, three, four, six, eight, 12 and 24.

Finding Factors Using Divisibility Rules

Divisibility rules are another tool that you can use to calculate the factors of a number. Though the rules may not give you every single factor, especially for larger numbers, they give you a great place to start. Here are some of the divisibility rules you can use to calculate the factors for 24. Note that this is not a comprehensive list of divisibility rules and only contains rules that yield a factor for 24.

One divisibility rule states that any integer is divisible by one. This means that you always need to list the number one and the provided number as factors.

Another divisibility rule states that any even number is divisible by two. An even number is an integer that ends in zero, two, four, six or eight. Using this rule, we know that 24 is divisible by two and whatever number you multiply by two to get 24.

For the number three, you know that a number is divisible by three when all of its digits add up to an integer that’s divisible by three. With the number 24, two plus four equals six, which is divisible by three. You know that three and another number are factors of 24.

To see if a number is divisible by four, you can take the last two digits of the number and see if they’re divisible by four. The number 24 only has two digits, but 24 is divisible by four. This means four and another number will multiply to give you 24.

You can determine if a number is divisible by six by checking that the number is even and divisible by three. The number 24 satisfies both these requirements, so you know it’s divisible by six.

To see if a number is divisible by 12, you must determine if it’s divisible by three and four. If it meets the rules of divisibility for the numbers three and four, this also means it’s divisible by 12. The number 24 is divisible by three and four, so it’s also divisible by 12.

Checking Your Work

Once you have a list of factors, you can check that all the numbers are indeed factors by multiplying the factor by the number that yields the specified number. For example, if you want to check that three is a factor of 24, multiply it by eight and make sure you get 24 as your answer.

How to Use Factors

Factors are commonly used in algebra and calculus problems. You might also need to use the factors of a number when you need to divide a number into even portions. This gives factoring real-life utility.

Assume that you’ve made 100 cookies and want to pass them out to some of your friends. Although you aren’t quite sure how many friends you want to give cookies to, you want to make sure that each friend gets at least five cookies and receives no more than 10 cookies. It’s possible to use factors to find numbers that meet your criteria.

For example, the numbers five and 20 multiply together to equal 100. This means that you can give five cookies to 20 of your friends. You can also multiply 10 by 10 to equal 100. Another option is to hand out 10 cookies to 10 of your friends.