Notes on Special Numbers

A number is a fundamental concept in mathematics.Numbers are used for counting, measuring, keeping things in order, indexing, and so on. Natural numbers, whole numbers, rational and irrational numbers, integers, real numbers, complex numbers, even and odd numbers, and so on are examples of distinct sorts of numbers based on their qualities. We can ascertain the result by applying the basic fundamental arithmetic operations on integers. Prior to the advent of numbers, tally marks were utilised. A number (N) is considered a special number if the total of its factorial of digits is equal to the number itself.

Types of Numbers

The qualities of distinct sorts of numbers determine their classification. Natural numbers, for example, begin with 1, whereas whole numbers begin with 0, prime numbers that are only divisible by 1, and the number itself, and so on. In the next sections, we’ll study more about the various forms of numbers.

Consecutive Numbers

Numbers that follow each other in order from lowest to greatest are known as consecutive numbers. Every two numerals are normally separated by a single digit.

Natural Numbers and Whole Numbers

A natural number is a positive integer that is never less than zero. The letter N is used to signify it. It’s worth noting that whole numbers have no decimal or 

fractional parts. They are called by the ‘W’ letter.

Even Numbers and Odd Numbers

Even numbers are ones that can be divided into two equal groups or pairs and are divisible by 2 perfectly. Examples include 2, 4, 6, 8, 10, and so on. To put it another way, they are whole integers that are divisible by two exactly.

Odd numbers are full numbers that cannot be split by two completely. There’s no way to pair these digits together. All entire numbers, with the exception of multiples of 2, are odd numbers.

Prime Numbers and Composite Numbers

The number which have only two factors I.e., one and the number itself is called prime number. Prime numbers include 2, 5, 7, 11, and so forth. A prime number is defined as any whole number bigger than one that has exactly two elements, one and itself. Now we know that a prime number is made up of only two factors: 1 and the number itself.

A composite number contains more than two parts, meaning it may be divided by the number 1 and itself, as well as at least one other integer. Any number greater than 1 that is not a prime number is considered a composite number. There are always more than two elements in composite numbers.

Co-prime Numbers

Co-prime numbers are pairs of numbers that have no common factor other than one. In other terms, co-primes are a set of numbers or integers that have just 1 as a common factor, implying that their highest common factor (HCF) is 1. Mutually prime numbers are also known as relatively prime numbers. In order to form co-primes, there must be two numbers.

Perfect Numbers

These are positive integers that except for the number itself and they are equal to the sum of their components. Perfect numbers, in other terms, are positive integers that are the sum of their proper divisors. The lowest perfect number is 6, which has the following divisors: 1, 2 and 3.

Cardinal numbers

“How many” is expressed with a cardinal number. Because they display the amount, cardinal numbers are sometimes known as “counting numbers.”

Ordinal numbers

Ordinal numbers indicate the order of items in a collection?first, second, third, and so on. Quantity is not represented by ordinal numbers. They just show position or rank.

Nominal numbers

What does a nominal number denote? a phone number, a member of a sports team Nominal numbers do not indicate quantity or position. They’re just used to identify things.

Properties of Number

The following are the basic mathematical properties of numbers:

• The commutative property of numbers applies to both addition and multiplication. a + b = b + a and a x b = b x a are the formulas.
• Addition and multiplication are both affected by the associative property of integers. It’s written like this: a + (b + c) = (a + b) + c, and a x (b x c) = (a x b) x c.
• The sum of two numbers plus a third number equals the sum of the products of each addend and the third number. a x  (b + c) = a x b + a x c is how it’s written.
• Identity Property: We have a multiplicative identity of 1 and an additive identity of 0. a + 0 = a and a x 1 = an are the formulas.

Conclusion

On a daily level, we all deal with numbers. These are utilised in a variety of ways, including mathematical computations, phone numbers, and phone calls, account identification, money exchange, and cooking.