Introduction to Number System for Placement Exams
types of numbers, natural numbers, integers, rational numbers, irrational numbers, prime numbers, composite numbers
Introduction to Number System for Placement Exams
The number system is the backbone of quantitative aptitude for placements. Almost every placement exam — whether TCS, Infosys, Wipro, or Accenture — tests your understanding of numbers at the foundational level. Mastering this topic gives you an edge in solving problems faster and more accurately.
Types of Numbers
Natural numbers are positive counting numbers starting from 1. Whole numbers include zero along with all natural numbers. Integers extend whole numbers to include negative values as well. Rational numbers can be expressed as p divided by q where q is not zero, covering all fractions and terminating decimals. Irrational numbers like the square root of 2 and pi cannot be expressed as fractions.
Prime and Composite Numbers
A prime number is divisible only by 1 and itself. The primes begin 2, 3, 5, 7, 11, 13. The number 1 is neither prime nor composite — it is a special case. A composite number has more than two factors; examples include 4, 6, 8, 9, and 15. The number 2 is the only even prime number.
Key Rules
To check if a number N is prime, test divisibility only up to the square root of N. All prime numbers greater than 3 are of the form 6k plus or minus 1. The sum of the first n natural numbers equals n multiplied by n plus 1, divided by 2.
Solved Example
Which of the following is NOT a prime number — 11, 21, 29, 37? Check 21: it equals 3 multiplied by 7, so it is divisible by 3 and 7, making it composite. The numbers 11, 29, and 37 are each divisible only by 1 and themselves. Answer: 21 is not a prime number.
Interview Tips
In placement interviews and aptitude rounds, number system questions often appear as part of data sufficiency or number series problems. Always double-check prime number identification by testing divisibility up to the square root of the number. Practice mental classification of numbers daily to build the speed required for actual placement tests.