Factors Of 48 – Definition And Prime Factorization - Vedantu

The concept of factors of 48 is important in mathematics, helping students solve problems quickly and improve their foundation for topics like HCF, LCM, and prime factorization. Recognizing the factors of 48 will also aid in exam preparation, mental math, and real-life calculations.

What Are Factors of 48?

A factor of 48 is any whole number that divides 48 exactly without leaving a remainder. Factors are part of many maths topics such as divisibility, prime factorization, and number properties. Understanding factors of 48 is useful for solving HCF, LCM, and even algebraic factorization questions.

List of All Factors of 48

The complete list of factors of 48 (positive integers) is:

• 1
• 2
• 3
• 4
• 6
• 8
• 12
• 16
• 24
• 48

These are the numbers by which 48 can be divided exactly. For example, 48 ÷ 8 = 6 (no remainder), so both 8 and 6 are factors of 48.

Prime Factorization of 48

The prime factorization of 48 expresses 48 as a product of prime numbers. Let’s write the steps below:

1. 48 ÷ 2 = 24
2. 24 ÷ 2 = 12
3. 12 ÷ 2 = 6
4. 6 ÷ 2 = 3
5. 3 is a prime number

So, the prime factors of 48 are: 2 × 2 × 2 × 2 × 3 = 24 × 3

This process is also shown using a factor tree:

Step	Breakdown
1	48 = 2 × 24
2	24 = 2 × 12
3	12 = 2 × 6
4	6 = 2 × 3
5	Prime numbers: 2, 2, 2, 2, 3

Pair Factors of 48

Pair factors are two numbers whose product is 48. The pair factors of 48 are helpful for multiplication and division problems:

Factor 1	Factor 2
1	48
2	24
3	16
4	12
6	8

Remember, negative pairs (like -1 × -48 = 48) also exist, but usually only positive factors are listed unless the question asks for all integers.

Properties and Quick Facts About Factors of 48

• Factors of 48 are both even (like 2, 4, 6, 8, 12, 16, 24, 48) and odd (1, 3).
• 48 is a composite number since it has more than two factors.
• The sum of all positive factors of 48 is 124.
• All factors of 48 are divisors of 48 (they divide 48 exactly).

The concept of factors of 48 is widely used in HCF, LCM, and number property questions for school and competitive exams.

Step-by-Step: How to Find All Factors of 48

Follow these steps to list all factors of 48:

1. Write 1 × 48 (since 1 and 48 multiply to 48). 2. 2 × 24 (2 divides 48 exactly). 3. 3 × 16 4. 4 × 12 5. 6 × 8 6. Write the numbers in order to list all: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

Speed Trick: Fast Listing of Factors

For quick exams, check divisibility by all numbers up to the square root of 48 (~7). For each divisor, write its pair. If you divide 48 by a number and get a whole number, both are factors.

Example: 48 ÷ 8 = 6. So, both 6 and 8 are factors.

Vedantu’s live classes show such quick tricks to speed up factor-finding!

Related Topics to Practice

• Factors of 24
• Factors of 36
• Factors and Multiples
• Factors of 72

Try These Yourself

• List all even factors of 48.
• Which prime numbers are factors of 48?
• Find a pair of factors of 48 whose sum is 14.
• Check if 24 is a factor of 48.

Common Mistakes to Avoid

• Missing factors by skipping numbers during division.
• Not matching each factor with a pair (for example, listing 6 but forgetting 8).
• Counting duplicates or listing negative factors unless asked.

Summary Table: All You Need!

Type	Value
Total positive factors	10
List of factors	1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Prime factorization	24 × 3
Pair factors	(1,48), (2,24), (3,16), (4,12), (6,8)
Sum of factors	124

Classroom Tip

To quickly check if a number is a factor of 48, divide 48 by that number. If the result is a whole number, it is a factor. Vedantu’s expert teachers recommend practicing such checks with similar numbers for a strong understanding.

We covered the factors of 48 from definition to prime factorization, pair factors, and easy shortcuts. Keep practicing with Vedantu's resources and related topics to strengthen your basics in Maths and prepare for exams confidently!