Real Numbers — Formula Sheet

a = bq + r, 0 ≤ r < b

HCF(c,d) = HCF(d,r)

HCF(a,b) × LCM[a,b] = a × b

LCM = product of greatest power of each prime factor

HCF = product of smallest power of each common prime factor

Terminating decimal ↔ denominator in simplest form has only prime factors 2 and/or 5

If q has prime factorisation 2^n 5^m, then the decimal terminates

If q is not of the form 2^n 5^m, then the decimal is non-terminating repeating

If p is prime and p divides a^2, then p divides a

Examples of irrational numbers include √2, √3, √15, π, and 0.10110111011110....