Quant: Number System

Number Systems forms the base for quant ability and clearing of concepts is important for CAT and other related exams. Following table gives a brief introduction to system of numbers.

Prime Number

Starting from the basic knowledge, a prime number is a natural number which has only two distinct divisors: 1 and itself.
The number 1 is not a prime number.
There are 25 prime numbers under 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.


Prime Factorization Theorem: This is the area where prime numbers are used. This theorem states that any integer greater than 1 can be written as a unique product of prime numbers.
Examples:


Thus, prime numbers are the basic building blocks of any positive integer. This factorization will also help in finding GCD and LCM quickly.

Perfect Numbers

A number is a perfect number if the sum of its factors, excluding itself and but including 1, is equal to the number itself.

Example: 6 (1 + 2 + 3 = 6), 28 (1 + 2 + 4 + 7 +14 = 28)

Co-Prime Numbers

Two numbers are co-prime to each other, if they do not have any common factor except 1.

Example: 25 and 9, since they don’t have a common factor other than 1

Points to Remember

1. The number 1 is neither prime nor composite.
2. The number 2 is the only even number which is prime.
3. (xⁿ + yⁿ) is divisible by (x + y), when n is an odd number.  
4. (xⁿ – yⁿ) is divisible by (x + y), when n is an even number.  
5. (xⁿ – yⁿ) is divisible by (x – y), when n is an odd or an even number.                                                                                                                                                                                      Next