Factors of 24: Complete Guide with Factor Pairs & Prime Factorization

Factors are numbers that divide another number evenly, without anything left over. This guide walks through what the factors of 24 are, how to find them using three different methods, and why they matter. You will also see common factors, prime factors, factor pairs, and worked examples to build your understanding step by step.

What Are the Factors of 24?

A factor is a number that divides into another number evenly, with nothing left over. For 24, the complete set of positive factors is 1, 2, 3, 4, 6, 8, 12, and 24. Below, we break these down into common factors, prime factors, factor pairs, and more.

Common Factors of 24

Common factors are factors that two or more numbers share. To find them, list all the factors of each number and look for the ones that appear on every list.

The largest of these common factors is the greatest common factor, or GCF. For 24 and 36, the GCF is 12. For 24 and 48, the GCF is 24. This concept becomes useful when you need to simplify fractions or break problems into smaller parts.

Prime Factors of 24

Prime factors are factors that are also prime numbers. A prime number has exactly two distinct factors: 1 and itself. The first few prime numbers are 2, 3, 5, 7, and 11.

To find the prime factors of 24, list all its factors and pick out the primes. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among these, 2 and 3 are prime numbers. So the prime factors of 24 are 2 and 3.

Notice that 4, 6, 8, and 12 are also factors of 24, but they are not prime because each has more than two factors.

Prime Factorization of 24

Prime factorization means rewriting a number as a product of only prime numbers. Every whole number greater than 1 has one unique prime factorization. This is sometimes called the Fundamental Theorem of Arithmetic.

To find the prime factorization of 24, divide by the smallest prime number that goes into it evenly.

The result is 2 × 2 × 2 × 3, which can be written more simply as 2³ × 3.

This compact form tells you exactly which prime numbers make up 24 and how many times each one appears.

Positive Factors of 24

Positive factors are the positive whole numbers that divide a given number evenly. For 24, the complete list of positive factors is:

• 1
• 2
• 3
• 4
• 6
• 8
• 12
• 24

Every one of these numbers divides 24 without leaving a remainder. You can check this by dividing 24 by each one. If the result is a whole number, it is a factor.

Factor Pairs of 24

A factor pair is two numbers that multiply together to give the original number. For 24, each pair multiplies to 24.

Notice that the pairs mirror each other. Once you pass the square root of 24, which is about 4.9, the pairs start repeating in reverse order. That is why you only need to check numbers up to 4 or 5.

How to Find Factors of 24?

Find Factors of 24 Using the Prime Factorization Method!

The prime factorization method uses the prime factors of a number to generate all of its factors. Here is how it works for 24.

Step 1: Write 24 as a product of prime factors. You already know that 24 = 2³ × 3.

Step 2: List all the possible combinations of these prime factors. Start with the smallest exponents and work up.

For 2³, the powers are 2⁰, 2¹, 2², and 2³. For 3¹, the powers are 3⁰ and 3¹.

Step 3: Multiply each power of 2 by each power of 3.

Step 4: Collect all the results. You get 1, 2, 4, 8, 3, 6, 12, and 24.

Step 5: Arrange them in order from smallest to largest. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

You can also use prime factorization to count how many factors a number has without listing them all. For 24 = 2³ × 3¹, add 1 to each exponent and multiply the results: (3 + 1) × (1 + 1) = 4 × 2 = 8. This tells you that 24 has 8 positive factors.

Find Factors of 24 Using the Multiplication Method!

The multiplication method is one of the simplest ways to find factors. You look for pairs of whole numbers that multiply to give 24. Start with 1 and work your way up.

Step 1: Start with 1. Multiply it by a number to get 24. Since 1 × 24 = 24, write down 1 and 24.

Step 2: Move to 2. Multiply 2 by something to get 24. 2 × 12 = 24, so write down 2 and 12.

Step 3: Try 3. 3 × 8 = 24, so write down 3 and 8.

Step 4: Try 4. 4 × 6 = 24, so write down 4 and 6.

Step 5: Try 5. There is no whole number that multiplies by 5 to make 24, so skip it.

Step 6: Stop when you reach a number you already wrote down. You already have 6 from the pair (4, 6), so you are done.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

This method works best when you work in order and stop once you reach a repeating number. It is quick and does not require any division.

Find Factors of 24 Using the Rainbow Method!

The rainbow method is a visual way to find factor pairs. You draw pairs on opposite sides of a rainbow arc, which helps you see when you have found all the factors.

Step 1: Write the number 24 at the center of your page.

Step 2: Start with 1 on the left side. Pair it with 24 on the right side. Draw a curved line connecting them.

Step 3: Move to 2 on the left. Pair it with 12 on the right. Draw another curved line.

Step 4: Move to 3 on the left. Pair it with 8 on the right. Draw another curved line.

Step 5: Move to 4 on the left. Pair it with 6 on the right. Draw another curved line.

Step 6: Try 5. It does not work, so skip it.

Step 7: The next number is 6. You already have 6 on the right side, so you are done.

The factor pairs you found are:

The rainbow method is especially helpful for visual learners. The arcs show you when all pairs have been found, and you can easily see if you missed any numbers.

Solved Examples of Factors of 24

Example 1: What Are the Prime Factors of 24?

Question: What are the prime factors of 24?

Solution: Start with the full list of factors for 24: 1, 2, 3, 4, 6, 8, 12, and 24. From this list, pick out the numbers that are prime. A prime number has exactly two factors: 1 and itself.

Answer: The prime factors of 24 are 2 and 3.

You can also find this by using prime factorization. Since 24 = 2³ × 3, the prime factors are clearly 2 and 3.

Example 2: What Are the Negative Factors of 24?

Question: What are the negative factors of 24?

Solution: Every positive factor has a corresponding negative factor. Multiplying two negatives gives a positive product, so any negative number that divides 24 will also work.

Answer: The negative factors of 24 are -1, -2, -3, -4, -6, -8, -12, and -24.

These negative factors also form pairs. For example, -2 × -12 = 24. So the negative factor pairs are (-1, -24), (-2, -12), (-3, -8), and (-4, -6).

Conclusion

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The prime factorization is 2³ × 3, and the prime factors are 2 and 3. You can find these factors using the prime factorization method, the multiplication method, or the rainbow method. Each approach gives the same result and helps reinforce your number sense.

Understanding factors prepares you for more advanced topics like greatest common factor (GCF) and least common multiple (LCM). These ideas show up in fraction work, algebra, and even competition math.

At WuKong Math, our structured program helps students build strong number sense through interactive lessons and real-world examples. With a curriculum that spans foundational math to AMC 8 and Math Kangaroo prep, we guide learners step by step toward math confidence. Try a free math trial class today!

Mastering Factors and Multiples

In many school math programs, learning about factors and multiples begins in upper elementary and continues into middle school. Two important standards that cover these skills are:

4.OA.B.4 – Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is prime or composite.

6.NS.B.4 – Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor.

Mastering factors and factor pairs gives students a solid foundation for working with fractions, simplifying expressions, and solving problems efficiently.

Frequently Asked Questions on Factors of 24

Q1: What is the greatest common factor (GCF) of 24 and 36?

The GCF of 24 and 36 is 12.

Q2: What are the factor pairs of 24?

The positive factor pairs are (1, 24), (2, 12), (3, 8), and (4, 6). The negative factor pairs are (-1, -24), (-2, -12), (-3, -8), and (-4, -6).

Q3: Is 24 a prime number?

No, 24 is not a prime number. It has more than two factors, so it is a composite number.

Factor Reference Table

James | WuKong Math Teacher

Graduated from Columbia University in the United States and has rich practical experience in mathematics competitions’ teaching, including Math Kangaroo, AMC… He teaches students the ways to flexible thinking and quick thinking in sloving math questions, and he is good at inspiring and guiding students to think about mathematical problems and find solutions.