Number Theory: Prime Numbers, Factor Trees, and Building Blocks of Numbers
Every whole number has unique structural properties. A 'factor' is a number that divides another number exactly without leaving a remainder. A 'multiple' is the product of multiplying a number by any whole number (1, 2, 3... ). A 'prime number' is a whole number strictly greater than 1 that has exactly two distinct factors: 1 and itself (such as 2, 3, 5, 7, 11... ). In this lesson, students master the 'Factor Tree' method to decompose composite numbers into their unique prime factors.
🌳 Prime Factorization via Factor Trees
Factor Tree for 24:
24 = 4 × 6 = (2 × 2) × (2 × 3)
Prime factors of 24: 2 × 2 × 2 × 3.
Factor Tree for 36:
36 = 6 × 6 = (2 × 3) × (2 × 3)
Prime factors of 36: 2 × 2 × 3 × 3.
⭐ Key Number Facts:
- 2 is the smallest prime number and the ONLY even prime number.
- 1 is neither prime nor composite because it has only ONE factor.
- The number 1 is a common factor of all numbers.
- The number 0 is a common multiple of all numbers.
Write the prime factorization of 30.
Answer: 30 = 2 × 3 × 5.
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