Real Numbers

Every composite number can be expressed

Every composite number can be expressed as a product of primes, and this factorization is unique (except for the order of factors). For example: 60 =

Step

Step-by-step process: 1) Draw factor tree by dividing by smallest prime, 2) Continue until all factors are prime, 3) Write as product of prime powers.

HCF = Product of lowest powers

HCF = Product of lowest powers of common prime factors. Example: For 72 = 2³ × 3² and 48 = 2⁴ × 3, HCF = 2³ × 3¹ = 24. Take only the primes that appea

LCM = Product of highest powers

LCM = Product of highest powers of all prime factors present. Example: For 72 = 2³ × 3² and 48 = 2⁴ × 3, LCM = 2⁴ × 3² = 144. Include all primes from

For any two positive integers

For any two positive integers a and b: HCF(a,b) × LCM(a,b) = a × b. Example: For 72 and 48, HCF = 24, LCM = 144, and 24 × 144 = 72 × 48 = 3456. This r