Number classification hierarchy: Natural Numbers (N = {1,2,3,...}), Whole Numbers (W = {0,1,2,3,...}), Integers (Z = {...,-2,-1,0,1,2,...}), Rational Numbers (Q = p/q where q≠0, includes terminating and repeating decimals), Irrational Numbers (cannot be expressed as p/q — non-terminating, non-repeating decimals like √2, √3, π, e), Real Numbers (R = Q ∪ Irrational — all points on number line). Relationship: N ⊂ W ⊂ Z ⊂ Q ⊂ R.

Fundamental Theorem of Arithmetic: Every positive integer greater than 1 can be expressed as a UNIQUE product of prime numbers (ignoring order). This process IS called prime factorization (REET trick says 'cannot be' — wrong). Example: 420 = 2² × 3 × 5 × 7. Application: Finding HCF (product of common prime factors with lowest powers) and LCM (product of all prime factors with highest powers). Key relationship: HCF × LCM = Product of two numbers.

HCF-LCM problem solving: Given LCM = 495, HCF = 5, sum = 100. Let numbers be 5a and 5b where HCF(a,b) = 1. Then 5a + 5b = 100, so a + b = 20. Also LCM = 5ab = 495, so ab = 99. From a+b=20 and ab=99: a=9, b=11 (or vice versa). Numbers: 45 and 55. Difference = 10.

Euclid's Division Lemma: For any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b. Used for finding HCF through Euclid's Division Algorithm (repeatedly dividing until remainder = 0). Example: HCF(455, 42): 455 = 42×10 + 35, then 42 = 35×1 + 7, then 35 = 7×5 + 0. So HCF = 7.

Constants exist in TWO primary forms: Absolute constants (fixed value in all contexts — π = 3.14159..., e = 2.71828..., g = 9.8 m/s²) and Arbitrary constants (parameters that remain fixed in a given context but can vary between contexts — like 'c' in y = mx + c where c is constant for a specific line but varies across different lines).

REET Exam Tips: 7 questions. Focus on: number classification hierarchy (which set contains which), HCF-LCM relationship formula (HCF × LCM = Product), Fundamental Theorem of Arithmetic (every number = unique prime product), and Euclid's Division Lemma. The HCF-LCM word problem is asked in almost every paper.