Number System

Mathematics · 6 min read · Sunitha Rao

Classification of numbers, divisibility rules and remainder basics.

The number system is the foundation of the quantitative aptitude section. Numbers are classified as natural numbers, whole numbers, integers, rational and irrational numbers. Almost every arithmetic chapter builds on these definitions, so clarity here saves time later.

In exams the most productive areas are divisibility rules, unit-digit questions, and finding remainders. A number is divisible by 3 when its digit sum is divisible by 3, and by 9 when the digit sum is divisible by 9. For 11, take the difference between the sum of digits in odd and even positions.

Prime numbers deserve special attention: 2 is the only even prime, and there are 25 primes below 100. Learning them by heart removes a whole category of mistakes.

Important points

Natural numbers start at 1; whole numbers include 0.
Divisible by 4 if the last two digits form a multiple of 4.
Divisible by 8 if the last three digits form a multiple of 8.
There are 25 prime numbers below 100.
LCM x HCF = product of the two numbers.

Key formulas

LCM(a,b) x HCF(a,b) = a x b

Number of factors: if N = p^a x q^b then factors = (a+1)(b+1)

Examples

Is 3,168 divisible by 9? Digit sum = 3+1+6+8 = 18, which is divisible by 9, so yes.
HCF of 24 and 36 is 12, LCM is 72. Check: 12 x 72 = 864 = 24 x 36.