How to Find and List All Factors of 24 Easily
The concept of factors of 24 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding the factors of a number helps students with topics like division, multiples, prime factorization, and solving real-world problems such as arranging groups or finding common divisors. Let’s learn all about the factors of 24 with Vedantu’s easy and clear explanation!
What Is Factors of 24?
A factor of 24 is any whole number that divides 24 exactly, leaving no remainder. In simple terms, if you can multiply two whole numbers together to get 24, then both those numbers are factors of 24. This concept is essential for understanding prime numbers, common multiples, and carrying out division in school maths and daily life situations.
List of All Factors and Factor Pairs of 24
The factors of 24 are the numbers you can evenly divide 24 by. Below is a complete list, including their positive and negative pairings:
| Positive Factors | Factor Pair |
|---|---|
| 1 | 1 × 24 |
| 2 | 2 × 12 |
| 3 | 3 × 8 |
| 4 | 4 × 6 |
| 6 | 6 × 4 |
| 8 | 8 × 3 |
| 12 | 12 × 2 |
| 24 | 24 × 1 |
All positive factors: 1, 2, 3, 4, 6, 8, 12, and 24.
All negative factors: -1, -2, -3, -4, -6, -8, -12, and -24.
Prime Factorization of 24
Prime factorization is breaking down a composite number into a product of its prime numbers. Here are the steps to find the prime factors of 24:
1. Divide 24 by the smallest prime, 2: 24 ÷ 2 = 122. Divide 12 by 2: 12 ÷ 2 = 6
3. Divide 6 by 2: 6 ÷ 2 = 3
4. 3 is a prime number, so: 3 ÷ 3 = 1
So, the prime factorization of 24 is 2 × 2 × 2 × 3 or \( 2^3 \times 3^1 \).
Prime factors of 24: 2 and 3.
How to Find Factors of 24 (Step-by-Step Illustration)
- Start with 1 and 24: 1 × 24 = 24
- Test divisibility: 24 ÷ 2 = 12, so 2 and 12 are factors.
- Next, 24 ÷ 3 = 8, so 3 and 8 are factors.
- 24 ÷ 4 = 6, so 4 and 6 are factors.
- Try 5: 24 ÷ 5 = 4.8 (not a whole number) – not a factor.
- Continue up to √24 (~4.9), you get all unique pairs!
Key Formula for Number of Factors
To find the total number of factors, use the formula: If \( n = a^x \times b^y \), then number of factors = (x+1)(y+1). For 24: \( 2^3 \times 3^1 \) → (3+1) × (1+1) = 4 × 2 = 8 factors.
Relation to Other Numbers
Comparing factors of 24 with numbers like 18, 30, or 36 builds an understanding for LCM, HCF, and patterns in multiplication. See these for more examples: Factors of 36, Factors of 18, Factors of 30.
Real-Life Applications
Factors of 24 help with dividing objects equally (like sharing 24 chocolates among friends), arranging seats in groups, or in tiling, packaging, and planning events. Understanding factors supports logical thinking and problem-solving.
Speed Trick or Vedic Shortcut
A quick check: If an even number divides 24, or the individual digits of 24 (2+4=6) show divisibility by 3, use this in exams to spot factors without full division.
Vedantu teachers often show factor trees visually, making learning fun and speedy in live classes!
Try These Yourself
- Write all the factors of 24.
- Find the factor pairs of 24 (both positive and negative).
- What is the prime factorization of 24?
- Is 7 a factor of 24?
- Name three numbers with more factors than 24.
Frequent Errors and Misunderstandings
- Mixing up factors and multiples (multiples of 24 are different from its factors!).
- Missing out negative factors (for advanced levels).
- Counting repeated pairs like (4,6) and (6,4) separately (they’re the same pair).
Solved Examples
Example 1: List all the factors of 24.
1. Start with 1 and 24.2. Next, 2 × 12 = 24.
3. Then 3 × 8 = 24.
4. Then 4 × 6 = 24.
5. List all: 1, 2, 3, 4, 6, 8, 12, 24.
Example 2: Find the prime factors of 24.
1. Divide 24 by 2: 24 ÷ 2 = 12.2. Divide 12 by 2: 12 ÷ 2 = 6.
3. Divide 6 by 2: 6 ÷ 2 = 3.
4. 3 is a prime: 3 ÷ 3 = 1.
5. Final prime factors: 2, 2, 2, 3 (or \( 2^3 \times 3^1 \)).
Practice Questions
- Write all factors of 24 in pairs.
- List all prime factors of 24.
- Is 6 a factor of 24?
- Is 5 a factor of 24?
- List two real-life uses of factors of 24.
Quick Revision Table
| Type | Values |
|---|---|
| Total Factors | 8 |
| All Factors | 1, 2, 3, 4, 6, 8, 12, 24 |
| Prime Factors | 2, 3 |
| Factor Pairs | (1;24), (2;12), (3;8), (4;6) |
| Prime Factorization | 2 × 2 × 2 × 3 or 2³ × 3 |
Internal Links — Related Pages for More Practice
We explored factors of 24—definition, pairs, prime factorization, solved questions, common mistakes, and real-life use. Keep practicing with Vedantu’s trusted learning resources to boost your confidence in maths!
FAQs on Factors of 24 – Complete Guide with Table, Pairs & Prime Factorization
1. What are the factors of 24?
The factors of 24 are the whole numbers that divide 24 exactly without leaving a remainder. These are: 1, 2, 3, 4, 6, 8, 12, and 24.
2. How many factors does 24 have?
The number 24 has a total of eight factors.
3. What is the prime factorization of 24?
The prime factorization of 24 is 2 × 2 × 2 × 3, which can also be written as 2³ × 3. This means 24 is composed of three factors of 2 and one factor of 3.
4. What are the factor pairs of 24?
The factor pairs of 24 are pairs of numbers that multiply together to equal 24. These are: (1, 24), (2, 12), (3, 8), and (4, 6). Remember that these pairs can also be negative: (-1, -24), (-2, -12), (-3, -8), and (-4, -6).
5. How do I find the factors of a number?
To find the factors of any number, systematically divide the number by each whole number starting from 1, up to the number itself. If the division results in a whole number (no remainder), then the divisor is a factor. For example, with 24: 24 ÷ 1 = 24; 24 ÷ 2 = 12; 24 ÷ 3 = 8; and so on.
6. What are the prime factors of 24?
The prime factors of 24 are the prime numbers that, when multiplied together, equal 24. These are 2 and 3.
7. What is a factor tree, and how can I use it for 24?
A factor tree is a visual method to find the prime factorization of a number. For 24, you start with 24, then break it down into its factors (e.g., 2 and 12). Continue breaking down composite factors (like 12) until you only have prime numbers. A factor tree for 24 might show branches leading to 2, 2, 2, and 3.
8. What is the difference between factors and multiples?
Factors are numbers that divide a given number exactly, while multiples are numbers obtained by multiplying a given number by whole numbers. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, while the multiples of 24 are 24, 48, 72, 96, and so on.
9. Are there negative factors of 24?
Yes, there are negative factors of 24. For every positive factor, there's a corresponding negative factor. For instance, since 2 is a factor, -2 is also a factor.
10. How are factors of 24 used in real-life situations?
Factors are useful in various real-world scenarios. For example, if you have 24 cookies and want to divide them equally among friends, understanding the factors helps determine the number of friends you can share with (1, 2, 3, 4, 6, 8, 12, or 24 friends).
11. What are some examples of numbers that share common factors with 24?
Many numbers share common factors with 24. For example, 12 (common factors 1, 2, 3, 4, 6, 12), 36 (common factors 1, 2, 3, 4, 6, 12), and 48 (common factors 1, 2, 3, 4, 6, 8, 12, 24) all share factors with 24.
12. Can you explain the concept of proper factors?
Proper factors of a number are all its factors except the number itself. For 24, the proper factors are 1, 2, 3, 4, 6, 8, and 12. The number 24 is excluded.
