Factors Of 225 That Add Up To 30

Factors of 225 That Add Up to 30: A Mathematical Exploration

This article explores the factors of 225 and how to find the pairs that sum up to 30. Understanding factor pairs is a fundamental concept in number theory with applications in algebra and other areas of mathematics. We'll break down the process step-by-step, making it easy to understand even for those with a basic grasp of mathematics.

First, let's identify the factors of 225. Factors are numbers that divide evenly into a larger number without leaving a remainder. The factors of 225 are: 1, 3, 5, 9, 15, 25, 45, 75, and 225.

Now, the challenge is to find two of these factors that add up to 30. We can approach this systematically:

Finding the Factor Pairs

We can list out the factor pairs and check their sums:

• 1 + 225 = 226
• 3 + 75 = 78
• 5 + 45 = 50
• 9 + 25 = 34
• 15 + 15 = 30

Aha! We've found our solution. The factor pair of 15 and 15 adds up to 30.

Understanding the Significance

This seemingly simple problem demonstrates an important concept in mathematics: factorization. Finding the factors of a number allows us to understand its structure and relationships with other numbers. This is crucial in many mathematical operations, including simplification of fractions, solving equations, and understanding prime factorization.

Expanding the Concept: Applications and Further Exploration

The ability to find factor pairs with specific sums has practical applications in various mathematical contexts:

• Solving quadratic equations: Finding factors is a key step in solving many quadratic equations.
• Simplifying algebraic expressions: Identifying common factors helps simplify complex expressions.
• Number theory problems: Many number theory problems involve finding specific factor pairs that meet particular conditions.

This problem also opens up avenues for further exploration. For instance, you could try finding factor pairs of other numbers that add up to a specific target sum. This exercise strengthens your understanding of number relationships and develops problem-solving skills.

Conclusion

We've successfully identified the factors of 225 and found the pair that adds up to 30: 15 and 15. This exercise highlights the importance of understanding factors and their relationships, a fundamental concept with broader applications in mathematics and beyond. Remember, practicing these types of problems helps build your mathematical intuition and problem-solving abilities.