Factor Trees and Prime Factorization

Every whole number (1) is either prime or a product of primes. The factor tree makes this visible: 24 breaks to 2 × 12, then 12 to 2 × 6, then 6 to 2 × 3, until only primes remain. The child discovers the fundamental theorem of arithmetic.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Algebra
• Level: Ages 9-10

Objectives

• Decompose a number into its prime factors using a factor tree
• Identify prime numbers up to 100
• Compute greatest common factor and least common multiple
• Prepare for number theory and fraction simplification

Materials

• Large paper for drawing factor trees
• List of primes 2–100
• Colored pencils
• Multiplication chart

Instructions

1. Choose a number: 24. 2. Write 24 at the top. 3. Find any two factors: 2 × 12. Write 2 and 12 below. 4. Circle 2 (prime). 5. Factor 12: 2 × 6. Circle 2. 6. Factor 6: 2 × 3. Circle both. 7. Read the primes: 2 × 2 × 2 × 3 = 2³ × 3. 8. Verify: 8 × 3 = 24. 9. Use factorizations to find GCF (24 and 36 share 2² × 3 = 12).

Educator tip

Different factor paths give the same primes — let children notice this surprising truth. Celebrate it as a theorem.

Assessment

Note complete factorization, identification of primes, and GCF/LCM calculation.

More from Mathematics

• Addition Snake Game
• Subtraction Snake Game
• Multiplication Snake Game
• Decanomial Bead Bar Layout (Short Form)
• Introduction to Negative Numbers
• Area of a Rectangle — Formula from Counting
• Area of a Triangle — Half the Rectangle
• Circumference and Pi — Measuring the Circle