Real Numbers — Formula Sheet

32760 = 2^3 × 3^2 × 5 × 7 × 13

123456789 = 3^2 × 3803 × 3607

a^2 = (p1p2...pn)(p1p2...pn) = p1^2p2^2...pn^2

Let p be a prime number. If p divides a^2, then p divides a, where a is a positive integer.

HCF(a, b) × LCM(a, b) = a × b

HCF(6, 20) = 2

LCM(6, 20) = 60

96 = 2^5 × 3, 404 = 2^2 × 101

HCF(96, 404) = 4

For any two positive integers a and b, a can be written as a = bq + r, where 0 is less than or equal to r and r is smaller than b.

A composite number x can be written as x = p1 p2 ... pn, where the primes are listed in ascending order.