Question

How do you find the composite numbers from 1 to 50 ?

Answer 1

Hint:The basic definition of the Composite numbers is that the numbers which have more than two factors, that is 1 and the number itself. Or you can say that all the natural numbers which are obviously not prime numbers and also divisible by more than two numbers are composites . The trick to identifying whether the number is prime or not is by checking that the divisor of that number should be ‘1’ and the number itself can never have more than two factors .

Complete Step by Step solution :
Furthermore, here is a table given with its prime factorization done which justifies that the integers which can be calculated by multiplying the two smallest positive integers and also containing at least one divisor other than number ‘1’ and itself .

There are two types of Composite numbers we can say as follows-
Odd Composite Numbers -
All the odd (numbers not divisible by 2) integers along with not having properties of prime numbers are best known as Odd Composite Numbers .
For instance, the integers which satisfy the above conditions of the definition 9 and 15 are Odd Composite Numbers.
Even Composite Numbers -
All the even (numbers divisible by 2) integers along with not having properties of prime numbers are best known as Even Composite Numbers . For instance, the integers which satisfy the above conditions of the definition 4, 10 and 12 are Even Composite Numbers.
The list of composite numbers from 1 to 50 are:
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50.

The reason of this will be more clear by prime factorisation given below of each number from 1 to 50
\[\begin{array}{*{20}{l}}
{{\mathbf{Composite}}{\text{ }}{\mathbf{Numbers}}}&{{\mathbf{Prime}}{\text{
}}{\mathbf{Factorisation}}} \\
4&{2{\text{ }} \times {\text{ }}2} \\
6&{2{\text{ }} \times {\text{ }}3} \\
8&{2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}2} \\
9&{3{\text{ }} \times {\text{ }}3} \\
{10}&{2{\text{ }} \times {\text{ }}5} \\
{12}&{2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}3} \\
{14}&{2{\text{ }} \times {\text{ }}7} \\
{15}&{3{\text{ }} \times {\text{ }}5} \\
{16}&{2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}2} \\
{18}&{2{\text{ }} \times {\text{ }}3{\text{ }} \times {\text{ }}3} \\
{20}&{2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}5} \\
{21}&{3{\text{ }} \times {\text{ }}7} \\
{22}&{2{\text{ }} \times {\text{ }}11} \\
{24}&{2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}3} \\
{25}&{5{\text{ }} \times {\text{ }}5} \\
{26}&{2{\text{ }} \times {\text{ }}13} \\
{27}&{3{\text{ }} \times {\text{ }}3{\text{ }} \times {\text{ }}3} \\
{28}&{2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}7} \\
{30}&{2{\text{ }} \times {\text{ }}3{\text{ }} \times {\text{ }}5} \\
{32}&{2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}2{\text{ }}
\times {\text{ }}2} \\
{33}&{3{\text{ }} \times {\text{ }}11} \\
{34}&{2{\text{ }} \times {\text{ }}17} \\
{35}&{5{\text{ }} \times {\text{ }}7} \\
{36}&{2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}3{\text{ }} \times {\text{ }}3} \\
{38}&{2{\text{ }} \times {\text{ }}19} \\
{39}&{3\;{\text{ }} \times {\text{ }}13} \\
{40}&{2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}5} \\
{42}&{2{\text{ }} \times {\text{ }}3{\text{ }} \times {\text{ }}7} \\
{44}&{4{\text{ }} \times {\text{ }}11} \\
{45}&{3{\text{ }} \times {\text{ }}3{\text{ }} \times {\text{ }}5} \\
{46}&{2{\text{ }} \times {\text{ }}23} \\
{48}&{2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}3} \\
{49}&{7{\text{ }} \times {\text{ }}7} \\
{50}&{2{\text{ }} \times {\text{ }}5{\text{ }} \times {\text{ }}5}
\end{array}\]

Note: The basic definitions of the terms Odd , Even , Prime , Composite Numbers and factors should be clear.
i) Zero is neither considered as prime nor composite number as it is not having any factors.
ii) “4” can be considered as the smallest composite number.
iii) “9” can be considered as smallest odd composite number
iv) “1” cannot be considered a composite number as it is having the sole divisor of 1 that is 1.
v) Any even number which is greater than 2 is a composite number.