Question

Write all the composite numbers between 10 and 35.

Answer 1

Hint:
Here, we will be using the various divisibility rules to easily identify the numbers that are not prime. A prime number is a number divisible by only 1 and itself. A composite number is a number which is not a prime number, that is it is divisible by 1, itself, and some other numbers as well.

Complete step by step solution:
We know that in the number system, prime numbers are the numbers which have only two factors, 1 and the number itself. Hence, it is obvious that they will be divisible by 1 and the number itself.
Composite numbers are the numbers which are not prime numbers. They are divisible by at least one more factor other than 1 and themselves.
We will use divisibility rules to easily identify the composite numbers between 10 and 35.
The numbers between 10 and 35 are 11, 12, 13, …, 32, 33, 34.
Now, we check the divisibility by 2.
We know that all even numbers are divisible by 2.
Hence, we can include the even numbers 12, 14, 16, …, 32, 34 to get the list of composite numbers between 10 and 35.
Now, we check the divisibility by 5.
All numbers that end with the digit 0 or 5 are divisible by 5.
Thus, the numbers 15, 20, 25, 30 are divisible by 5.
Hence, we can include the numbers 15, 20, 25, 30 to the list.
The list of composite numbers so far is 12, 14, 15, 16, 18, 20, 22, 24, 25, 26, 28, 30, 32, 34.
We will include the multiples of 3 to this list.
The multiples of 3 between 10 and 35 are 12, 15, 18, 21, 24, 27, 30, 33.

Therefore, the composite numbers between 10 and 35 are 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34.

Note:
In this problem, we have used the divisibility rule to find the numbers. Divisibility rule is a way of finding whether a number is completely divisible by another number or not without actually dividing the number. We can easily find the numbers that are not prime, that is composite using the divisibility rule. We can also use the multiples of prime numbers between 10 and 35 and include them to get the list of all the composite numbers between 10 and 35.