Question

What are the composite numbers between 20 and 40?

Answer 1

Hint: We must remember that if a number is divisible by more than two numbers, or if the number is divisible by any number other than 1 and itself, then that number is called a composite number. To check whether a number is prime or composite, we can divide that number successively with smaller numbers.

Complete step-by-step solution:
We know that if a number is only divisible by 1 and itself, then the number is called a prime number. And all numbers which are divisible by any other number other than 1 and itself, is called a composite number.
So, the easiest way to find composite numbers between any two numbers is to divide each number successively by 2, 3, 4, … till the number itself, and check if it is divisible by any other number or not.
Here, in this question we need to find the composite numbers between 20 and 40.
So, let us start with the number 20, and divide it with numbers starting from 2.
The number 20 is divisible by 2, so it is a composite number.
The number 21 is divisible by 3, so it is a composite number.
The number 22 is divisible by 2, so it is a composite number.
The number 23 is not divisible by any number other than 1 and 23, so it is a prime number.
The number 24 is divisible by 2, so it is a composite number.
The number 25 is divisible by 5, so it is a composite number.
The number 26 is divisible by 2, so it is a composite number.
The number 27 is divisible by 3, so it is a composite number.
The number 28 is divisible by 2, so it is a composite number.
The number 29 is not divisible by any number other than 1 and 29, so it is a prime number.
The number 30 is divisible by 2, so it is a composite number.
The number 31 is not divisible by any number other than 1 and 31, so it is a prime number.
The number 32 is divisible by 2, so it is a composite number.
The number 33 is divisible by 3, so it is a composite number.
The number 34 is divisible by 2, so it is a composite number.
The number 35 is divisible by 5, so it is a composite number.
The number 36 is divisible by 2, so it is a composite number.
The number 37 is not divisible by any number other than 1 and 37, so it is a prime number.
The number 38 is divisible by 2, so it is a composite number.
The number 39 is divisible by 3, so it is a composite number.
The number 40 is divisible by 2, so it is a composite number.
So, we have the list of composite numbers between 20 and 40 as 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39 and 40.

Note: We must notice that all even numbers are divisible by 2. Hence, we can say that all even numbers are composite numbers. By using this information, we can reduce the number of tests we have to make. Also, we must remember the divisibility rules of each number to solve this question much faster.