How many prime numbers are less than 100?
Understand the Problem
The question is asking for the total count of prime numbers that are less than 100. Prime numbers are those greater than 1 that have no positive divisors other than 1 and themselves. To solve this, we will identify and count all the prime numbers in that range.
Answer
25
Answer for screen readers
There are 25 prime numbers less than 100.
Steps to Solve
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List Possible Prime Candidates Start by listing the natural numbers less than 100. The candidates are: $$ 2, 3, 4, 5, 6, 7, \ldots, 99 $$
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Identify Prime Numbers Go through the list and identify which of these numbers are prime. A prime number is only divisible by 1 and itself.
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Check for Each Number Check each candidate:
- 2: Prime (only divisible by 1 and 2)
- 3: Prime (only divisible by 1 and 3)
- 4: Not prime (divisible by 1, 2, and 4)
- 5: Prime (only divisible by 1 and 5)
- 6: Not prime (divisible by 1, 2, 3, 6)
- 7: Prime (only divisible by 1 and 7)
Continue this up to 99.
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Count the Prime Numbers Once identified, count the total number of prime numbers. From our checks: The prime numbers less than 100 are: $$ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 $$
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Calculate the Total Count Count the total number of primes listed. There are 25 prime numbers less than 100.
There are 25 prime numbers less than 100.
More Information
Counting primes helps in understanding number theory and has applications in cryptography. The distribution of prime numbers is a fundamental topic in mathematics.
Tips
- Confusing composite numbers with prime numbers: Always check the divisibility of each candidate.
- Overlooking smaller prime numbers: Remember, 2 is the smallest and the only even prime.
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