The number of prime numbers which are less than 100 is
25
Finding Prime Numbers Less Than 100
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. To find the number of prime numbers less than 100, we need to list all such numbers starting from 2 and going up to 99, checking if each number meets the definition of a prime number.
Here is the list of prime numbers less than 100:
- 2 (only even prime number)
- 3
- 5
- 7
- 11
- 13
- 17
- 19
- 23
- 29
- 31
- 37
- 41
- 43
- 47
- 53
- 59
- 61
- 67
- 71
- 73
- 79
- 83
- 89
- 97
Let's count the numbers in this list carefully.
| Range | Prime Numbers | Count |
|---|---|---|
| 1-10 | 2, 3, 5, 7 | 4 |
| 11-20 | 11, 13, 17, 19 | 4 |
| 21-30 | 23, 29 | 2 |
| 31-40 | 31, 37 | 2 |
| 41-50 | 41, 43, 47 | 3 |
| 51-60 | 53, 59 | 2 |
| 61-70 | 61, 67 | 2 |
| 71-80 | 71, 73, 79 | 3 |
| 81-90 | 83, 89 | 2 |
| 91-100 | 97 | 1 |
Adding the counts from each range:
\(4 + 4 + 2 + 2 + 3 + 2 + 2 + 3 + 2 + 1 = 25\)
There are 25 prime numbers less than 100.
Revision Table: Prime Numbers up to 100
| Count | Prime Number |
|---|---|
| 1 | 2 |
| 2 | 3 |
| 3 | 5 |
| 4 | 7 |
| 5 | 11 |
| 6 | 13 |
| 7 | 17 |
| 8 | 19 |
| 9 | 23 |
| 10 | 29 |
| 11 | 31 |
| 12 | 37 |
| 13 | 41 |
| 14 | 43 |
| 15 | 47 |
| 16 | 53 |
| 17 | 59 |
| 18 | 61 |
| 19 | 67 |
| 20 | 71 |
| 21 | 73 |
| 22 | 79 |
| 23 | 83 |
| 24 | 89 |
| 25 | 97 |
Additional Information: Understanding Prime Numbers
Understanding prime numbers is fundamental in number theory. Here are some related concepts:
- Composite Number: A natural number greater than 1 that is not prime is called a composite number. Composite numbers have divisors other than 1 and themselves. Examples: 4 (divisors 1, 2, 4), 6 (divisors 1, 2, 3, 6).
- Number 1: The number 1 is neither prime nor composite. It only has one divisor, which is 1 itself.
- Sieve of Eratosthenes: This is an ancient algorithm used for finding all prime numbers up to a specified integer. It works by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2.
- Importance: Prime numbers are the building blocks of all natural numbers greater than 1, as stated by the Fundamental Theorem of Arithmetic (every integer greater than 1 is either a prime number itself or can be represented as the product of prime numbers).
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Important Questions from Integers
Find the value of \(\sqrt{2025}\) .
How many times does the number 5 occur in the range of numbers from 1 to 100?
A. 21
B. 22
C. 20
D. 19
A prime number
A. is not a positive integer.
B. has no divisor at all.
C. has only 1 and itself as divisors.
D. has more than two divisors.
__________ are twin prime number.
A. (4, 9)
B. (2, 3)
C. (4, 6)
D. (3, 5)A factory produced 18,58,509 cassettes in the month of January, 7623 more cassettes in the of February and owing to short supply of electricity produced 25,838 less cassettes in March than in February. Find the total production in all?
A. 55,57,312
B. 59,83,245
C. 55,64,935
D. 56,08,988
