Factors of 48

Factors are numbers that divide a given number exactly without leaving a remainder. Understanding factors helps in arithmetic, algebra, and number theory. In this article, we will explore the factors of 48, how to find them, their properties, and their applications in real life.

What are Factors?

A factor of a number is any number that divides it completely without leaving a remainder.

Example:

• 6 is a factor of 48 because 48 ÷ 6 = 8 (no remainder).
• 7 is not a factor of 48 because 48 ÷ 7 = 6.857 (remainder exists).

How to find the Factors of 48

To determine the factors of 48, find all the numbers that divide 48 without leaving a remainder.

Step-by-Step Method:

1. Start with 1 and 48: Every number is divisible by 1 and itself. So, 1 and 48 are factors.
2. Check divisibility:
   • 2 is a factor because 48 ÷ 2 = 24.
   • 3 is a factor because 48 ÷ 3 = 16.
   • 4 is a factor because 48 ÷ 4 = 12.
   • 6 is a factor because 48 ÷ 6 = 8.

Complete List of Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Prime Factorization of 48

Prime factorization is breaking a number into its smallest prime factors.

Steps for Prime Factorization:

• 48 ÷ 2 = 24
• 24 ÷ 2 = 12
• 12 ÷ 2 = 6
• 6 ÷ 2 = 3
• 3 is prime, so we stop here.

Prime Factorization of 48: 48 = 2 × 2 × 2 × 2 × 3 or 2⁴ × 3¹

Pair Factors of 48

Factors of a number can be grouped into pairs that multiply to give the number.

Factor Pairs of 48:

• (1,48)
• (2,24)
• (3,16)
• (4,12)
• (6,8)

Odd and Even Factors of 48

• Even factors: 2, 4, 6, 8, 12, 16, 24, 48
• Odd factors: 1, 3

Common Factors of 48 with Another Number

To find common factors, compare the factors of 48 with another number.

Example: Common Factors of 48 and 36:

• Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
• Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
• Common factors: 1, 2, 3, 4, 6, 12

Highest Common Factor (HCF) of 48 and Another Number

The HCF is the largest common factor between two numbers.

Example: HCF of 48 and 36: 12

Applications of Factors in Real Life

• Grouping objects: Helps decide possible group sizes.
• Arranging items in rows: Helps organize items efficiently.
• Finding LCM and HCF: Important for fractions, ratios, and algebra.

Conclusion

Understanding factors is fundamental in mathematics. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. We explored methods to find factors, prime factorization, factor pairs, and their applications. This knowledge is crucial for problem-solving in arithmetic and algebra.