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Common factors are numbers that divide exactly into two or more other numbers. When we simplify fractions, finding common factors is an essential step. In the fraction \(-\frac{55}{85y}\), both 55 and 85 have common factors. We look for these to help reduce the fraction to its simplest form.

To find common factors, start by listing the factors of each number. For 55, the factors are \[1, 5, 11, 55\], and for 85, they are \[1, 5, 17, 85\]. Notice that \(5\) appears in both lists. This means 55 and 85 share 5 as a factor.

Finding these shared factors simplifies calculations. It allows us to rewrite a fraction in its simplest form by dividing both the numerator and the denominator by their greatest common factor.

The greatest common factor (GCF) is the largest factor that two numbers have in common. In the process of simplifying fractions, identifying the GCF allows us to reduce the fraction to its simplest form efficiently.

In the fraction \(-\frac{55}{85y}\), we first found common factors. Among these, the greatest common factor of 55 and 85 is 5. Recognizing the GCF is essential because it ensures we simplify the fraction as much as possible in one step.

To use the GCF, we divide both the numerator (55) and the denominator (85) by 5. This operation offers a straightforward way to shrink the numbers involved while keeping the fraction equivalent. After doing this step, we get a fraction that looks simpler at first sight: \(-\frac{11}{17y}\), which is much easier to work with in further calculations or real-life applications.

Prime factorization involves breaking down a number into its basic building blocks called prime numbers. Prime numbers are numbers greater than 1 that can only be divided evenly by 1 and themselves—examples include 2, 3, 5, 7, and so forth.

To understand how factorization aids in simplifying fractions like \(-\frac{55}{85y}\), start by finding the prime factors of each number. For 55, its prime factorization is \(5 \times 11\). For 85, the prime factorization is \(5 \times 17\).

The shared prime factor here is \(5\). This revelation shows the greatest common factor because it's the highest value multiplying into both numbers. By understanding prime factorization, we can easily identify these commonalities. By dividing the fraction's numerator and denominator by their greatest common factor (from their prime elements), we simplify to the most basic form, \(-\frac{11}{17y}\), such that no further reduction is possible.