We are talking about a very fundamental and basic topic here in this article, Number System. Quantitative Aptitude begins with the concept of Number System. Let us understand the most important points in Number System first.
What all you should know?
You should know the following things to get a hold on Number System:
1. Types of Numbers
2. What are Prime numbers
3. Properties Of Numbers
4. Properties of Integers
5. Decimals and Fractions
7. Divisibility Rules
9. LCM and HCF
10. Remainder Theorem
Introduction: The number system that we use is the decimal number system that has ten numbers from 0 to 9. It can be represented in a number line as shown below.
Types of numbers:
There are many kinds of numbers each having its own properties and hence different from others. The following are the different kinds.
• Complex Numbers
- Real and Imaginary Numbers
• Real Numbers
- Rational and Irrational numbers (also Decimals)
• Rational numbers
- Integers and Fractions
- Even and Odd (Negative & Positive) and Whole numbers
• Whole Numbers
- Zero and Natural Numbers
• Natural Numbers
- Even & Odd Numbers (and also Prime & Composite Numbers)
A fraction has two parts namely a numerator and a denominator to denote the parts of a whole number.
Points to remember:
- 1 is neither a prime nor a composite number but an odd number not even.
- 2 is the lowest prime number and the only even prime number
- 3 is the lowest odd prime number
- When a prime number greater than or equal to 5 (>5) is divided by 6, it gives a remainder of either 1 or 5. But any number greater than or equal to 5 (>5) when divided by 6, giving remainder of either 1 or 5 is not necessarily prime.
- All prime numbers can be represented by the form (6x + 1) or (6x - 1). Any number that can be represented in the form (6x + 1) or (6x - 1) is not necessarily a prime number.
If the product of numbers (P X Q X R X S) is divided by N, then the remainder will be equal to that of the product of the individual remainders when divided by the same dividend.
Few Divisibility Rules:
All whole numbers are divisible by 1.
All even numbers are divisible by 2.
A number is divisible by 5 if it ends in 0 or 5 and is a non-zero number.
In order to check the divisibility of a number by a composite number, divide the composite divisor into prime factors and then check for its divisibility with each. For example, to check the divisibility of a number with 12, break down 12 into 3 and 4.