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Learn math for CAT

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
6. Exponents
7. Divisibility Rules
8. Factorization
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
• Integers
- Even and Odd (Negative & Positive) and Whole numbers
• Whole Numbers
- Zero and Natural Numbers
• Natural Numbers
- Even & Odd Numbers (and also Prime & Composite
Numbers)
Fractions:
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.
Remainder Theorem:
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.

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