Natural numbers are a part of real numbers. A set of natural numbers is usually denoted by the symbol N.
Some useful facts about natural numbers are as given below:
- Natural numbers are often referred to as counting numbers. The most basic method of representing the natural number is to use fingers another method is the tally mark for each thing or object.
- The natural number 1 is the only positive integer that is neither prime nor composite.
- The sum of First n natural numbers is given using following formula:
Sn = [n(n + 1)]/2
- The sum of squares of the first n natural number is given by:
Sn = [n(n + 1)(2n + 1)]/6
- The smallest natural number is 1 and there is no largest natural number.
- Natural numbers are closed under addition and multiplication. This means that the sum or product of any two natural numbers is also a natural number.
- Natural numbers can be ordered and compared. For any two natural numbers a and b, either a < b, a=b, or a > b.
- The factorial number is denoted as n! Is the product of positive integers from 1 to n. Suppose we are asked to find out the 4!, then we can say 4! = 4 × 3 × 2 × 1 = 24.
- For any natural number n, formula for factorial is given as: n! = n × (n - 1) × (n - 2) × . . . × 1.
- A natural number is considered perfect if it is equal to the sum of its proper divisors (excluding itself). The smallest perfect number is 6 (1 + 2 + 3 = 6), followed by 28 (1 + 2 + 4 + 7 + 14 = 28).
- Natural numbers can form triangular numbers, which are the sums of the first n natural numbers. The nth triangular number is given by the formula
T_n = \frac{n(n + 1)}{2} . For example, the first few triangular numbers are 1, 3, 6, 10, and 15.
- Some natural numbers read the same backward as forward (e.g., 121, 1331).
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