Factors of 24 Explained with Complete Factor List

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 = 12

2. 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)

1. Start with 1 and 24: 1 × 24 = 24
2. Test divisibility: 24 ÷ 2 = 12, so 2 and 12 are factors.
3. Next, 24 ÷ 3 = 8, so 3 and 8 are factors.
4. 24 ÷ 4 = 6, so 4 and 6 are factors.
5. Try 5: 24 ÷ 5 = 4.8 (not a whole number) – not a factor.
6. 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

• Factors of 36
• Factors of 30
• Prime Factors
• LCM and HCF
• Factors of 18

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!