The number of divisors of $540$ is _____.

Introduction of Numbers

1. Natural Numbers: These are the numbers ($1, 2, 3,$ etc.) that are used for counting.

2. Whole Numbers: The set of numbers that includes all natural numbers and the number zero are called whole numbers. Whole numbers are also called as Non negative integers.

3. Prime Numbers: A natural number larger than $1$ is a prime number if it does not have other divisors except for itself and $1$. (The lowest prime number is $2$. $2$ is also the only even prime number. The lowest odd prime number is $3$.)

4. Composite Numbers: It is a natural number that has at least one divisor different from unity and itself.

5. Even Numbers: An even number is an integer that can be divided by two and remain an integer or has no remainder.

6. Odd Numbers: An integer that is not an even number is an odd number.

7. Divisibility by 2 or 5: A number is divisible by $2$ or $5$ if the last digit is divisible by $2$ or $5$.

8. Divisibility by 3 (or 9): All such numbers the sum of whose digits are divisible by $3$ (or $9$) are divisible by $3$ (or $9$).

9. Divisibility by 4: A number is divisible by $4$ if the last $2$ digits are divisible by $4$.

10. Divisibility by 6: A number is divisible by $6$ if it is simultaneously divisible by $2$ and $3$ .

11. Divisibility by 8: A number is divisible by $8$ if the last $3$ digits of the number are divisible by $8$.

12. Divisibility by 11: A number is divisible by $11$ if the difference of the sum of the digits in the odd places and the sum of the digits in the even places is either zero or is divisible by $11$.

13. Divisibility by 12: All numbers divisible by $3$ and $4$ are divisible by $12$.

14. Divisibility by 7, 11 or 13: The integer n is divisible by $7, 11$ or $13$ if and only if the difference of the number of its thousands and the remainder of its division by 1000 is divisible by $7, 11$ or $13$.

15. Products:

1. Odd $\times$ odd $=$ odd

2. Odd $\times$ Even$=$ Even

3. Even $\times$ Even $=$ Even

16. Simplification questions following the BODMAS rule.

B $=$ Bracket

O $=$ Of or order

D $=$ Division

M $=$ Multiplication

A $=$ Addition

S $=$ Subtraction

17. To solve the approximation question, convert decimal values to the nearest values (i.e. $123.33=123, 545.78=545)$.

18. If the questions based on square/cube and square/cube root try to convert the numbers into nearest perfect square/cube number.

19. Arithmetic Progression:

Let $a_1, a_2, a_3$, .........an is an AP of '$n$' terms

(i) $n$th term $\left(a_n\right)=a+(n-1)d$

(ii) sum of '$n$' terms $=\frac{n}{2}\left[2a+(n-1)d\right]$

20. Geometric Progression:

Let $a_1, a_2, a_3$, ......... $a_n$ is an GP of '$n$' terms

(i) Common ratio $\left(r\right)=\frac{a_n}{a_{n-1}}$

(ii) $n$th term $={ar}^{n-1}$, where '$a$' is the first term and '$r$' is the common ratio

(iii) $S_n=\left[\frac{\left(r^n-1\right)}{\left(r-1\right)}\right]$, where $r>1$

OR

(iv) $S_n=\left[\frac{\left(1-r^n\right)}{\left(1-r\right)}\right]$, where $r<1$