What are Numbers?
A number is a mathematical object used to count and measure. In the Hindu-Arabic system of numbers, there are ten digits. These are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Types of Numbers
Numbers are of different types :
A number is a mathematical object used to count and measure. In the Hindu-Arabic system of numbers, there are ten digits. These are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Types of Numbers
Numbers are of different types :
- Natural Numbers - Counting numbers are called natural numbers
- Whole Numbers - Counting numbers including 0 (zero) are called whole numbers.Integers - Counting numbers, 0 (zero) and negative numbers together form the integers.
Even and Odd Numbers
- Even Numbers - A natural number divisible by 2 is called an even number.
- Odd Numbers - A natural numbers not divisible by 2 is called an odd number.
Prime Numbers
A natural number greater than 1 which has no other factors other than 1 and itself is called a prime number.
Composite Numbers
A natural number greater than 1 which is not a prime number is called a composite number.
Co-prime Numbers
Two natural numbers x and y are said to be co-prime if their HCF is 1.
Divisibility Tests
a) Divisibility by 2 - A number is divisible by 2 if its units digit is 0, 2, 4, 6 or 8.
b) Divisibility by 3 - A number is divisible by 3 if sum of digits of the number is divisible by 3.
c) Divisibility by 4 - A number is divisible by 4 if sum of its last two digits is divisible by 4.
d) Divisibility by 5 - A number is divisible by 5 if the last digit of the number is either 0 or 5.
e) Divisibility by 8 - A number is divisible by 8 if the last three digits of the number is divisible by 8.
f) Divisibility by 9 - A number is divisible by 9 if the sum of its digits is divisible by 9.
g) Divisibility by 10 - A number is divisible by 10 only when the last digit of the number is 0.
h) Divisibility by 11 - A number is divisible by 11 only if the difference between the sum of its digits at odd place (Odd Numbers) and the sum of its digits at even place (Even Numbers) is either 0 or a number divisible by 11.
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A natural number greater than 1 which has no other factors other than 1 and itself is called a prime number.
Composite Numbers
A natural number greater than 1 which is not a prime number is called a composite number.
Co-prime Numbers
Two natural numbers x and y are said to be co-prime if their HCF is 1.
Divisibility Tests
a) Divisibility by 2 - A number is divisible by 2 if its units digit is 0, 2, 4, 6 or 8.
b) Divisibility by 3 - A number is divisible by 3 if sum of digits of the number is divisible by 3.
c) Divisibility by 4 - A number is divisible by 4 if sum of its last two digits is divisible by 4.
d) Divisibility by 5 - A number is divisible by 5 if the last digit of the number is either 0 or 5.
e) Divisibility by 8 - A number is divisible by 8 if the last three digits of the number is divisible by 8.
f) Divisibility by 9 - A number is divisible by 9 if the sum of its digits is divisible by 9.
g) Divisibility by 10 - A number is divisible by 10 only when the last digit of the number is 0.
h) Divisibility by 11 - A number is divisible by 11 only if the difference between the sum of its digits at odd place (Odd Numbers) and the sum of its digits at even place (Even Numbers) is either 0 or a number divisible by 11.
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