What Are the 24 Factors?

One, two, three, four, six, eight, twelve, and twenty-four are the factors of 24. These are all integers that may be multiplied by another integer to produce the number 24. There are several methods for discovering all of a number’s factors.

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The Factor’s Definition

Any integer that may be evenly divided into another number is a factor. If you divide 20 by five, for example, five will evenly split 20 four times. When you split 20 by 11, however, 11 will only enter 20 once. It has a nine-digit remainder. A factor is any number that has a residue when divided by the provided integer.

Using the Prime Factors to Find Factors

To identify all the factors of a number, one way is to first find the number’s prime factors. A prime factor is one that is both a prime number and a factor. A prime number is one that can only be divided by itself and one.

Remember that every number is divisible by one and itself before you begin. To begin, you can say that one and 24 are factors of 24.

Two is the smallest prime number that divides evenly into the number 24. You may get 24 by multiplying two by twelve. You don’t need to do anything extra with two because it’s a prime number.

To discover further factors, you must locate the rest of the factors for the number 12. One, twelve, one, six, three, and four are all divisible by twelve. Because 24 is divisible by 12, it is also divisible by the factors of 12. One, two, three, four, six, twelve, and 24 should now be on your complete list of components for 24.

Because three times eight equals 24, the number 24 has another prime factor. Three has no factors other than one because it is a prime number. The number eight, on the other hand, has the following elements: one, eight, two, and four. This means that the list of factors for 24 needs to be expanded by eight. One, two, three, four, six, eight, twelve, and twenty-four are currently on the list.

Using Divisibility Rules to Find Factors

Another method for calculating a number’s factors is to use divisibility principles. Though the guidelines may not include every possible aspect, especially for higher numbers, they provide a good starting point. You may compute the factors for 24 using the following divisibility criteria. This is not an exhaustive list of divisibility rules; it only includes those that produce a factor of 24.

Any number is divisible by one, according to one divisibility rule. This means that the number one and the specified number must always be listed as factors.

Any even number is divisible by two, according to another divisibility rule. An even number is one that finishes in one of the following: zero, two, four, six, or eight. We know that 24 is divisible by two because we can multiply any number by two to get 24.

When all of a number’s digits add up to an integer divisible by three, you know it’s divisible by three. Two plus four equals six, which is divisible by three in the number 24. You already know that three and another number are 24 variables.

Take the last two digits of a number and divide them by four to discover if it’s divisible by four. Although the number 24 contains just two digits, it is divisible by four. This means multiplying four by another number to get 24.

You may check if a number is divisible by six by seeing if it is even and divisible by three. Because the number 24 meets both of these criteria, it is divisible by six.

Determine if a number is divisible by three and four to discover if it is divisible by 12. It is divisible by 12 if it fits the requirements of divisibility for the integers three and four. Because the number 24 is divisible by three and four, it may also be divided by twelve.

Examining Your Work

Once you have a list of numbers, you can verify if they are all factors by multiplying the factor by the number that returns the specified number. For instance, if you want to see if three is a factor of 24, multiply it by eight and check that the result is 24.

Factors and How to Use Them

In algebra and calculus, factors are frequently employed. When dividing a number into even portions, you may need to apply the factors of the number. This adds real-life utility to factoring.

Assume you’ve baked 100 cookies and want to share them with a few pals. You want to make sure that each friend gets at least five cookies and no more than ten cookies, even if you aren’t sure how many friends you want to gift cookies to. It’s possible to find numbers that meet your criteria by using factors.

For example, the numbers five and twenty add up to one hundred. This means you can gift each of your 20 pals five cookies. You may also divide 10 by ten to get 100. Another option is to give 10 cookies to ten different people.

Misha Khatri
Misha Khatri is an emeritus professor in the University of Notre Dame's Department of Chemistry and Biochemistry. He graduated from Northern Illinois University with a BSc in Chemistry and Mathematics and a PhD in Physical Analytical Chemistry from the University of Utah.

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