Definitions [17]
Even Number: A number ending in 0, 2, 4, 6, or 8 is an even number.
Odd Number: A number ending in 1, 3, 5, 7, or 9 is an odd number.
Numbers having more than two factors are called composite numbers. 4, 6, 8, 9, 10, and so on are examples of composite numbers.
If the difference between two coprime numbers is 2, the numbers are said to be twin prime numbers. For example: (3, 5)
A prime number is a natural number greater than 1 that has exactly two factors: 1 and the number itself.
2, 3, 5, 7, 11, and so on are examples of prime numbers.
A number is divisible by 2 if it has any of the digits 0, 2, 4, 6, or 8 in its ones place.
If the sum of the digits in a number is divisible by 3, then the number is divisible by 3.
A number is divisible by 5 if the digit in its units (ones) place is either 0 or 5.
A number is divisible by 4 if the last two digits of the given number are divisible by 4.
Note: If the last two digits of a number are “00”, then it is also divisible by 4.
A number is divisible by 6 if it is divisible by both 2 and 3.
A number is divisible by 9 if the sum of all its digits is also divisible by 9.
A number is divisible by 11 if the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) is either 0 or a multiple of 11.
Prime factors of a number are the prime numbers that divide it exactly.
A factor of a number is any number that divides the given number completely without leaving a remainder.
or
When two numbers are multiplied, the result is called their product, and the numbers that are multiplied are called factors of the product.
A common factor of two or more numbers is a number that divides each of the given numbers exactly, without leaving any remainder.
The HCF (Highest Common Factor) of two or more numbers is the highest number among all the common factors of the given numbers.
A number is called a multiple of another if it is exactly divisible by that number, i.e., the division leaves no remainder.
The least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers.
Concepts [19]
- Concept of Even and Odd Number
- Prime and Composite Numbers
- Eratosthenes’ Method of Finding Prime Numbers
- Tests for Divisibility of Numbers
- Divisibility by 2
- Divisibility by 3
- Divisibility by 5
- Divisibility by 4
- Divisibility by 6
- Divisibility by 8
- Divisibility by 9
- Divisibility by 10
- Divisibility by 11
- Prime Factorisation
- Factors and Common Factors
- Highest Common Factor (HCF)
- Multiples and Common Multiples
- Lowest Common Multiple
- Relationship between the Numbers and their HCF and LCM
