Question

What are the even composite numbers from $50$ to $80?$

Answer 1

Hint: In this question, we will first try to understand the definition of composite numbers. After that we will see what are the criteria of even composite numbers. We will write all the even composite numbers from $50$ to $80$ and then we will count them. By this way we will get our required answer.

Complete step by step answer:
Let us first understand the definition of composite numbers:
Composite numbers can be defined as natural numbers that have more than two factors. In other words we can say that any number that is divisible by a number other than $1$ and itself, are called composite numbers. Some examples of composite numbers are:
$4,6,8,9$ and so on.
In order to find the composite numbers, we should first find the factors of the given number. If the number has more than two factors, then the numbers are composite.
Now every even number that is not prime, is called an even composite number. We should keep in mind that every even composite has $2$ as its common factor.
So the best way to find the even composite numbers is to do the divisibility test. Divisibility test means that a number is divided evenly with no remainder.
Here we need to find the even composite numbers from $50$ to $80$ .
Let us start by writing the factors of $50$, we have:
$50 = 1,2,5,10,25,50$
We can see that this number has more than two factors and also $2$ as its factor. So this is an even composite number.
Now the factors of $51$ are:
$51 = 1,3,17,51$
Again this number also has more than two factors, but we can see that it does not have $2$ as its factors. So this is a composite number but it is not an even composite number.
Let us check the factors of $52$:
$52 = 1,2,4,13,26,52$
This number satisfies the criteria of even composite numbers, as it has more than two factors and $2$is also its factor. So this is also an even composite number.
Similarly, if we follow the above mentioned steps, we will be able to find even composite numbers between $50$ to $80$ .
So by using the above method, here is the list of all the even composite numbers between $50$ to $80$ :
$50,52,54,58,60,62,64,66,68,70,72,74,76,78,80$
Hence the total number of even composite numbers is $15$ .

Note:
 We should note that a perfect square is always composite. All the composite numbers that are not divisible by $2$ and have more than two factors, are called the odd composite numbers. We know that prime numbers are those numbers that have only two factors i.e. $1$and itself.
For example; $2,7,13,71...$ and so on.
We should note that $1$ is neither a prime nor composite number. And we can write all composite numbers as a product of prime numbers.