About 1 to 100 Prime Numbers
What are Prime Numbers?
The numbers having only two factors, that is, 1 and the number itself are called prime numbers.
For example:
(i) 7 is a prime number,
As it has only two factors, that is, 1 and 7.
(ii) 19 is a prime number,
And as 7, the number 19 is a prime number and has only two factors, 1 and 19.
List of Prime Numbers from 1 to 100
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Rapid Recall
Prime numbers up to 100 are;
Solved Examples
Example 1: From 1 to 100, John counted the first 10 prime numbers and Max counted the last 10 prime numbers, what will be the difference between the sum of their count?
Solution:
First 10 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Last 10 prime numbers are: 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Sum of first 10 prime numbers = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29
= 129
Sum of last 10 prime numbers = 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97
= 732
Difference = 732 – 129
= 603
Therefore, the difference between the first and last 10 prime numbers is 603.
Example 2: What is the average of the prime numbers between 1 and 20?
Solution:
Prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19
Numbers of prime numbers = 8
We know that, Average = \( \frac{\text{Sum of numbers}}{\text{Total number}} \)
Average = \( \frac{2 + 3 + 5 + 7 + 11 + 13 + 17 + 19}{8} \) [Addition]
= \( \frac{77}{8} \) [Division]
= 9.625
Therefore, the average of prime numbers between 1 and 20 is 9.625.
Example 3: Write the prime numbers between 20 and 40, and identify the count of these numbers?
Solution:
Prime numbers between 20 and 40 are 23, 29, 31, and 37.
Hence, there are 4 prime numbers between 20 and 40.
Prime numbers up to 100 are;
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Hence, there are 25 prime numbers from 1 to 100.
A composite number is a natural number with more than two factors.
For example:
(i) 6 : Factors of 6 = 1, 2, 3, and 6
Since the number 6 has more than two factors, it is a composite number.
(ii) 20 : Factors of 20 = 1, 2, 4, 5, 10, 20, and 40
Since the number 20 has more than two factors, it is a composite number.
The number 1 is a factor of every other number.
For example:
3 = 3 × 1
15 = 15 × 1 and so on.
From these observations, one can say that 1 is a factor of every number.
The factor of any number divides the number exactly without leaving any remainder.
For example:
14 ÷ 7 = 2.
As 7 divides the number 14 exactly 2 times without leaving any remainder, then 7 is a factor of 14.
The prime numbers are the numbers that have exactly two factors, that is, 1 and the number itself.
So, 2 is a prime number because it has exactly two factors, that are, 1 and 2.