Using the divisibility rule, divide the given number by $3$ and check if it is divisible by $3$ or not.

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(i) A factor of a number is that number which divides the number exactly.

(ii) A multiple of a number is exactly divisible by the number.

(iii) Every number is a factor as well as a multiple of itself.

(iv) $1$ is a factor of every number and is the only number, which has exactly one factor.

(v) Every number other than $1$ has at least two factors, namely $1$ and the number itself.

(vi) Every number other than $1$ can be uniquely expressed as the product of prime numbers, except for the order of prime numbers.

2. Prime Number:

A number having no factor other than $1$ and the number itself is called a Prime number. In other words, a Prime number has exactly two distinct factors, $1$ and the number itself.

3. Composite number:

(i) A number having factors other than $1$ and the number itself is called a Composite number.

(ii) The number $1$ is neither a Prime nor a Composite number, because it has a single factor.

4. Even and Odd Numbers:

(i) Numbers divisible by $2$ are called Even numbers.

(ii) Numbers not divisible by $2$ are called Odd numbers.

(iii) $2$ is the only even Prime number.

(iv) Every prime number other than $2$ is odd, but every odd number is not necessarily a prime number.

(v) Every even number greater than $4$ can be expressed as the sum of two odd prime numbers.

5. Twin Primes:

Primes occurring in pairs with a difference of two are called Twin primes.

6. Divisibility Test:

(i) A number is divisible by $2$, if the unit’s digit of the number is $0, 2, 4, 6 \mathrm{or} 8$.

(ii) A number is divisible by $3$, if the sum of the digits is divisible by $3$.

(iii) A number is divisible by $4$, if the number formed by its digits in ten’s and unit’s places is divisible by $4$.

(iv) A number is divisible by $5$, if unit’s digit is $0$ or $5$.

(v) A number is divisible by $6$, if it is divisible by both $2$ and $3$.

(vi) A number is divisible by $8$, if the number formed by its digits in hundred’s, ten’s and unit’s places is divisible by $8$.

(vii) A number is divisible by $9$, if the sum of the digits is divisible by $9$.

(viii) A number is divisible by $10$, if the unit’s digit is $0$.

(ix) A number is divisible by $11$, if the difference of the sum of its digits in odd places and the sum of its digits in even places (starting from unit’s place) is either $0$ or divisible by $11$.

7. $\mathrm{HCF}$ and $\mathrm{LCM}$:

(i) The $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ of two or more numbers is the largest number that divides all the given numbers.

(ii) The $\mathrm{L}.\mathrm{C}.\mathrm{M}.$ of two or more numbers is the smallest number which is divisible by all the given numbers.

8. Properties of $\mathrm{HCF}$ and $\mathrm{LCM}$:

(i) The product of $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ and $\mathrm{L}.\mathrm{C}.\mathrm{M}.$ of two numbers equals their product. This result may not be true for more than two numbers.

(ii) The $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ of any two prime or co-prime numbers equals $1$.

(iii) The $\mathrm{L}.\mathrm{C}.\mathrm{M}.$ of any two prime or co-prime numbers equals their product.

(iv) The $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ of two or more numbers is never greater than any of the numbers.

(v) The $\mathrm{L}.\mathrm{C}.\mathrm{M}.$ of two or more numbers is never less than any of the numbers.

(vi) The $\mathrm{H}.\mathrm{C}.\mathrm{F}.$ of two or more numbers is a factor of their $\mathrm{L}.\mathrm{C}.\mathrm{M}.$

(vii) If $x$ is a factor of $y$, then the $\mathrm{H}.\mathrm{C}.\mathrm{M}.$ of $x$ and $y$ is $x$ and $\mathrm{L}.\mathrm{C}.\mathrm{M}.$ of $x$ and $y$ is $y$.