Factoring Worksheets

Practice key concepts in Factoring with targeted worksheets covering equations, expressions, and problem-solving for Grades 6–12.

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A Parent’s Guide to Teaching Factoring

Factoring is a cornerstone of number sense and algebra. It supports simplifying fractions, finding common denominators, and solving problems efficiently. Use the routines and sequence below with our worksheets to build strong, flexible skills.

Big Ideas

  • Factors vs. multiples: factors divide a number exactly; multiples are skip-counts of a number.
  • Prime vs. composite: primes have exactly two factors (1 and itself); 1 is neither prime nor composite.
  • Prime factorization: every composite number can be written uniquely as a product of primes (up to order).
  • GCF & LCM: greatest common factor for splitting/grouping; least common multiple for synchronizing cycles and common denominators.

Concrete → Pictorial → Abstract

  • Concrete: arrays/rectangles, tiles, and counters to show factor pairs.
  • Pictorial: area models, factor trees, and Venn diagrams for prime exponents.
  • Abstract: divisibility rules, exponent notation, and efficient procedures.

Suggested Worksheet Sequence

  1. Prime & Composite Sorting — use divisibility rules (2, 3, 5, 9, 10) and arrays.
  2. Prime Factorization — factor trees; write with exponents (e.g., 84 = 22 × 3 × 7).
  3. Greatest Common Factor (GCF) — lists, prime exponents, Venn diagrams; apply to simplify ratios/fractions.
  4. Least Common Multiple (LCM) — skip counting, prime exponents, Venn diagrams; apply to schedules and common denominators.
  5. Applications — multi-step problems mixing GCF/LCM and fraction simplification.

Worked Examples

  • Factor lists: 24 → 1,2,3,4,6,8,12,24.
  • Prime factorization: 120 = 23 × 3 × 5; 360 = 23 × 32 × 5.
  • GCF: GCF(36, 60) = 12 (min exponents); GCF(18, 30, 42) = 6.
  • LCM: LCM(6, 8) = 24 (max exponents); LCM(12, 15) = 60.

Common Misconceptions & Fixes

  • Calling 1 prime: review definition; show 1 has only one factor.
  • Stopping too early: continue factoring until all factors are prime.
  • Mixing up GCF and LCM: use “GCF = largest shared factor” vs “LCM = first shared multiple.”
  • Skipping exponents: write prime powers to compare quickly and avoid errors.

Quick Daily Routines

  • Two-minute “factor flurry” (list factors of a target number).
  • Prime power warm-up: express 48, 72, 90 with exponents.
  • One GCF + one LCM mini-problem using prime exponents.

Extension to Algebra

  • Numeric → algebraic bridge: use GCF to factor expressions: 18x + 24 = 6(3x + 4).
  • Distributive property: connect area models for numbers to binomial “un-grouping.”

Conclusion: With visual models, prime-power reasoning, and steady practice, students gain a toolkit for GCF, LCM, and prime factorization—ready to extend naturally into algebra.