What Are The Factor Pairs Of 75

What are the Factor Pairs of 75? A Comprehensive Guide

Finding the factor pairs of a number is a fundamental concept in mathematics, crucial for understanding number properties and simplifying calculations. This article will delve into how to find all the factor pairs of 75, explain the process, and provide a clear understanding of what factor pairs represent. Learn how to identify factors and apply this knowledge to other numbers.

What are Factor Pairs?

Factor pairs are sets of two numbers that, when multiplied together, result in a specific target number. For example, the factor pairs of 12 include (1, 12), (2, 6), and (3, 4). Understanding factor pairs is essential for tasks like simplifying fractions, finding the greatest common factor (GCF), and solving various mathematical problems.

Finding the Factor Pairs of 75

To find the factor pairs of 75, we need to identify all pairs of numbers that multiply to 75. We can systematically approach this by starting with the smallest factor, 1:

1. Start with 1: Since 1 is a factor of every number, the first factor pair is (1, 75).

2. Check for Divisibility by 2: 75 is not an even number, so 2 is not a factor.

3. Check for Divisibility by 3: 75 is divisible by 3 (75 / 3 = 25), giving us the factor pair (3, 25).

4. Check for Divisibility by 5: 75 is clearly divisible by 5 (75 / 5 = 15), resulting in the factor pair (5, 15).

5. Continue the Process: We continue checking for divisibility by larger numbers. Since 15 is already included, we've essentially covered all the possible factors.

Therefore, the complete set of factor pairs for 75 are:

• (1, 75)
• (3, 25)
• (5, 15)

Understanding the Factors

The factors of 75 are 1, 3, 5, 15, 25, and 75. These are all the whole numbers that divide evenly into 75 without leaving a remainder. Notice how each factor in a pair is found in this list.

Applications of Factor Pairs

The concept of factor pairs is essential in various mathematical applications:

• Simplifying Fractions: Finding the greatest common factor (GCF) of the numerator and denominator requires identifying factor pairs.
• Algebraic Factoring: Factor pairs are crucial for factoring quadratic expressions and simplifying algebraic equations.
• Number Theory: Understanding factors helps in exploring concepts like prime factorization and divisibility rules.

By understanding the systematic approach to finding factor pairs, you can efficiently determine the factors of any number and apply this knowledge to various mathematical problems. Remember to always start with 1 and continue checking for divisibility until you’ve found all the pairs. This method provides a clear and efficient path to solving problems involving factor pairs.