Question

How many composite numbers are between 1 and 100?

Answer 1

Hint: Composite numbers are those natural numbers that are not prime and have more than two positive factors.

Complete step by step solution:
First of all, let us check how to determine the composite numbers:
Find all the factors of a given number.
If the number has more than two factors, then it is composite.
The best way to figure out if it is a composite number is to perform a divisibility test.
The rule states that a number is divisible by any composite number – if it is divisible by each of its factors.
Performing the divisibility test will help us to determine whether or not a number is a prime or composite number.
So, we need to find the composite number between 1 and 100. Let’s start –
Is 1 a composite number?
Let’s get its factors
Only 1 is the factor so it is not a composite number.
Is 2 a composite number?
Let’s get its factors
Only 1 and 2 are the factor so it is not a composite number.
Is 3 a composite number?
Let’s get its factors
Only 1 and 3 is the factor so it is not a composite number.
Is 4 a composite number?
Let’s get its factors
The factors of 4 are 1, 2, and 4. So it has 3 factors, which means 4 is the first composite number.
Is 5 a composite number?
Let’s get its factors
Only 1 and 5 is the factor so it is not a composite number.
Is 6 a composite number?
Let’s get its factors
The factors of 6 are 1, 2, 3, and 6. So it has 4 factors, which means 6 is the composite number.
Is 7 a composite number?
Let’s get its factors
Only 1 and 7 are the factor so it is not a composite number.
Is 8 a composite number?
Let’s get its factors
The factors of 8 are 1, 2, 4, and 8. So it has 4 factors, which means 8 is the composite number.
Is 9 a composite number?
Let’s get its factors
The factors of 8 are 1, 3, and 9. So it has 3 factors, which means 9 is the composite number.
Is 10 a composite number?
Let’s get its factors
The factors of 10 are 1, 2, 5, and 10. So it has 4 factors, which means 10 is the composite number.
So from 1 to 10, there are 5 composite numbers: 4, 6, 8, 9, and 10.
Similarly, if we follow the above-mentioned steps, we will be able to find the composite numbers between 1 and 100.
By using the above steps below is the list of composite numbers between 1 to 100 (including 1 and 100)
There are 74 composite number numbers between 1 to 100 (including 1 and 100)

Composite number between 1 to 10	4, 6, 8, 9, 10
Composite number between 11 to 20	12, 14, 15, 16, 18, 20
Composite number between 21 to 30	21, 22, 24, 25, 26, 27, 28, 30
Composite number between 31 to 40	32, 33, 34, 35, 36, 38, 39, 40
Composite number between 41 to 50	42, 44, 45, 46, 48, 49, 50
Composite number between 51 to 100	51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100

Note: A perfect square is always composite.
Every even composite number will have 2 as its factors.
Two composite numbers may be coprime or relatively prime.