Understanding Factors and GCF

Overview

This lecture explains what factors and common factors are, then details the meaning and usefulness of the greatest common factor, especially in simplifying fractions.

Factors and Factorization

• A factor is a whole number that multiplies with another to produce a given number.
• Numbers can have multiple factors; for example, 12 has factors 1, 2, 3, 4, 6, and 12.
• Every number has 1 and itself as factors, called "trivial factors."

Common Factors

• Common factors are factors shared by two or more numbers.
• To find common factors, list all factors of each number and identify the overlaps.
• Example: 12 and 42 share common factors 1, 2, 3, and 6.

The Greatest Common Factor (GCF)

• The greatest common factor is the largest factor that two numbers share.
• For 12 and 42, the GCF is 6.
• To find the GCF, list all factors of each number and choose the largest one in both lists.

Application: Simplifying Fractions

• The GCF is used to simplify fractions to their lowest terms.
• Divide both numerator and denominator by their GCF for simplest form.
• Example: 12/42 simplified by GCF (6) equals 2/7.

Key Terms & Definitions

• Factor — A whole number that divides another number evenly.
• Trivial Factors — The factors 1 and the number itself.
• Common Factor — A factor shared by two or more numbers.
• Greatest Common Factor (GCF) — The largest factor that two numbers have in common.

Action Items / Next Steps

• Practice finding factors, common factors, and the greatest common factor for various numbers.
• Try simplifying different fractions using their GCF.