Factors of 24 Explained: Pairs, Prime Factorization & More

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In math, “factors” are whole numbers that, when multiplied together, result in another number. Learning how to find these factors is a basic, yet important skill. So, what are the factors of 24?

This article answers that question! We’ll explore the factors of 24, how to find them, and a few ways you might use them. We’ll cover “pair factors,” prime factorization, and walk through some examples to show you how it all works.

What are factors of 24?

Factors are the whole numbers you can divide another number by without getting a remainder. So, the factors of 24 are all the whole numbers that divide evenly into 24.

Here’s the complete list:

  • 1
  • 2
  • 3
  • 4
  • 6
  • 8
  • 12
  • 24

As you can see, 24 has eight factors. Each of these numbers divides into 24 perfectly.

How to find the factors of 24

Here’s a simple method for finding the factors of 24:

Division method

  1. Start with the number 1 and then check each whole number in order. Divide 24 by 1, then 2, then 3, then 4, and so on.
  2. If the division results in a whole number, then the number you divided by is a factor of 24. For example:
    • 24 / 1 = 24
    • 24 / 2 = 12
    • 24 / 3 = 8
    • 24 / 4 = 6
    • 24 / 6 = 4
    • 24 / 8 = 3
    • 24 / 12 = 2
    • 24 / 24 = 1

Spotting factor pairs

As you look for factors, remember that factors often come in pairs. For example, 2 and 12 are a factor pair because 2 x 12 = 24.

You can stop looking for factors when you start seeing numbers you’ve already found. Once you reach a factor that you’ve already identified, you can be sure you’ve found all the factors.

What are the factor pairs of 24?

Factor pairs are just two numbers that, when multiplied together, equal 24. It’s that simple!

Let’s look at the positive factor pairs of 24:

  • 1 x 24 = 24 (so the pair is 1, 24)
  • 2 x 12 = 24 (so the pair is 2, 12)
  • 3 x 8 = 24 (so the pair is 3, 8)
  • 4 x 6 = 24 (so the pair is 4, 6)

But don’t forget about negative numbers! Remember, a negative number multiplied by another negative number gives you a positive number.

That means the negative factor pairs of 24 are:

  • -1 x -24 = 24 (so the pair is -1, -24)
  • -2 x -12 = 24 (so the pair is -2, -12)
  • -3 x -8 = 24 (so the pair is -3, -8)
  • -4 x -6 = 24 (so the pair is -4, -6)

Prime Factorization of 24

Okay, so what about prime factorization? That’s when you break a number down into a product of its prime factors. Remember that prime numbers are only divisible by 1 and themselves. Examples include 2, 3, 5, 7, and 11.

Here’s how you find the prime factorization of 24:

  1. Divide 24 by the smallest prime number, 2: 24 / 2 = 12
  2. Divide 12 by 2: 12 / 2 = 6
  3. Divide 6 by 2: 6 / 2 = 3
  4. Divide 3 by 3: 3 / 3 = 1

When you get down to 1, you’re done! The prime factorization of 24 is 2 x 2 x 2 x 3, which can also be written as 23 x 3.

Prime factorization and the number of factors

Prime factorization can help you figure out how many factors a number has. Here’s how it works:

  1. First, find the prime factorization. For 24, it’s 23 x 31.
  2. Then, add 1 to each exponent. So, (3+1) x (1+1) = 4 x 2.
  3. Finally, multiply those results: 4 x 2 = 8.

That means 24 has 8 factors.

This works because it accounts for all the possible combinations of the prime factors. Every factor of 24 is made up of some combination of 2s and 3s (or none at all), and this method covers all the bases.

What are multiples of 24?

A “multiple” of a number is what you get when you multiply that number by any whole number. So, if you multiply 24 by 1, 2, 3, 4, 5, and so on, the answers are multiples of 24.

Here are some examples:

  • 24
  • 48
  • 72
  • 96
  • 120

If a number is a factor of 24, then 24 is a multiple of that number. So, since 6 is a factor of 24, that means 24 is a multiple of 6.

Solved Examples on Factors of 24

Let’s look at some examples of problems involving factors of 24.

Example 1: Finding Common Factors

Problem: What are the common factors of 24 and 36?

Solution:

  • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
  • Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  • Common factors: 1, 2, 3, 4, 6, 12

Example 2: Candy Distribution

Problem: Sam has 24 candies to distribute equally among his friends. How many friends can he distribute the candies to without any leftovers?

Solution: Sam can distribute the candies to 1, 2, 3, 4, 6, 8, 12, or 24 friends.

Putting It All Together

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Knowing what they are and how to find them is a key skill in math.

Understanding factors helps you simplify fractions, solve algebraic equations, and get a better handle on number theory. It’s a basic building block for more advanced mathematical concepts.

So, keep exploring! The more you learn about factors and other areas of number theory, the stronger your math skills will become.