Prime Numbers up to 100
Prime numbers are the building blocks of all numbers. A prime number has exactly two factors: 1 and itself. In Class 4, you learn to identify all prime numbers up to 100 and use a method called the Sieve of Eratosthenes to find them.
There are exactly 25 prime numbers between 1 and 100. Knowing these primes helps in finding factors, simplifying fractions, and understanding number properties.
What is Prime Numbers up to 100 - Class 4 Maths (Factors and Multiples)?
A prime number is a whole number greater than 1 that has exactly two factors: 1 and the number itself.
A composite number has more than two factors.
1 is neither prime nor composite — it has only one factor (itself).
Prime number → Exactly 2 factors (1 and itself)
Composite number → More than 2 factors
Prime Numbers up to 100 Formula
All 25 prime numbers from 1 to 100:
| 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 |
Types and Properties
Key observations about prime numbers:
- 2 is the only even prime number. Every other even number is divisible by 2, so it has more than 2 factors.
- All prime numbers greater than 2 are odd. But not all odd numbers are prime (e.g., 9, 15, 21 are odd but composite).
- Twin primes are pairs of primes that differ by 2: (3,5), (5,7), (11,13), (17,19), (29,31), (41,43), (59,61), (71,73).
Solved Examples
Example 1: Example 1: Is 29 Prime?
Problem: Check if 29 is a prime number.
Solution:
Step 1: Try dividing 29 by 2, 3, 4, 5 (only need to check up to the square root of 29, which is about 5.4).
29 ÷ 2 = 14 remainder 1
29 ÷ 3 = 9 remainder 2
29 ÷ 4 = 7 remainder 1
29 ÷ 5 = 5 remainder 4
Step 2: 29 is not divisible by any number other than 1 and 29.
Answer: Yes, 29 is a prime number.
Example 2: Example 2: Is 51 Prime?
Problem: Check if 51 is a prime number.
Solution:
Step 1: Try dividing by small primes.
51 ÷ 3 = 17 (exact division, no remainder)
Step 2: Since 51 = 3 x 17, it has factors other than 1 and itself.
Answer: No, 51 is composite (factors: 1, 3, 17, 51).
Example 3: Example 3: Listing Primes Between Two Numbers
Problem: List all prime numbers between 30 and 50.
Solution:
Check each number: 31 (prime), 32 (even), 33 (÷3), 34 (even), 35 (÷5), 36 (even), 37 (prime), 38 (even), 39 (÷3), 40 (even), 41 (prime), 42 (even), 43 (prime), 44 (even), 45 (÷5), 46 (even), 47 (prime), 48 (even), 49 (÷7).
Answer: 31, 37, 41, 43, 47
Example 4: Example 4: The Only Even Prime
Problem: Why is 2 the only even prime number?
Solution:
Step 1: 2 has exactly 2 factors: 1 and 2. So it is prime.
Step 2: Every other even number (4, 6, 8, 10...) is divisible by 2. So they have at least 3 factors: 1, 2, and the number itself.
Answer: Every even number except 2 has 2 as a factor, making it composite. So 2 is the only even prime.
Example 5: Example 5: Word Problem
Problem: Rahul picks a number less than 20. It is prime and the sum of its digits is 8. What is the number?
Solution:
Step 1: Primes less than 20: 2, 3, 5, 7, 11, 13, 17, 19.
Step 2: Check digit sums: 17 → 1+7=8.
Answer: The number is 17.
Example 6: Example 6: Sum of First 5 Primes
Problem: Find the sum of the first 5 prime numbers.
Solution:
First 5 primes: 2, 3, 5, 7, 11
Sum = 2 + 3 + 5 + 7 + 11 = 28
Answer: 28
Example 7: Example 7: Twin Primes
Problem: Find all twin prime pairs between 1 and 20.
Solution:
Step 1: Twin primes differ by exactly 2.
Primes up to 20: 2, 3, 5, 7, 11, 13, 17, 19
Pairs differing by 2: (3,5), (5,7), (11,13), (17,19)
Answer: (3,5), (5,7), (11,13), (17,19)
Example 8: Example 8: Expressing as Sum of Two Primes
Problem: Express 30 as a sum of two prime numbers.
Solution:
Try different prime pairs:
7 + 23 = 30 (both prime)
11 + 19 = 30 (both prime)
13 + 17 = 30 (both prime)
Answer: 30 = 7 + 23 (also 11+19 or 13+17).
Example 9: Example 9: Is 91 Prime?
Problem: Is 91 a prime number?
Solution:
Step 1: Many students think 91 is prime, but check: 91 ÷ 7 = 13 (exact).
Step 2: 91 = 7 x 13, so it is composite.
Answer: No, 91 is not prime. It equals 7 x 13.
Key Points to Remember
- A prime number has exactly 2 factors: 1 and itself.
- 1 is not prime (it has only 1 factor).
- 2 is the only even prime number.
- There are 25 prime numbers from 1 to 100.
- To check if a number is prime, try dividing it by all primes up to its square root.
- Numbers like 51, 57, 87, 91 look prime but are not — always verify.
- Twin primes are pairs of primes that differ by 2.
Practice Problems
- Is 67 a prime number? Show your work.
- List all prime numbers between 40 and 60.
- Find the sum of all prime numbers between 10 and 20.
- Aditi says 57 is a prime number. Is she correct? Explain.
- Which is the largest prime number less than 80?
- Express 24 as a sum of two prime numbers.
- Find all twin prime pairs between 50 and 80.
- How many prime numbers have 3 as a digit (from 1 to 100)?
Frequently Asked Questions
Q1. Is 1 a prime number?
No, 1 is not a prime number. A prime number must have exactly 2 factors. The number 1 has only one factor (itself), so it is neither prime nor composite.
Q2. Why is 2 the only even prime number?
Every even number is divisible by 2. So any even number greater than 2 has at least three factors (1, 2, and itself), making it composite. Only 2 has exactly two factors.
Q3. How do you check if a large number is prime?
Divide the number by all prime numbers up to its square root. If none divide it evenly, the number is prime. For a number like 97, check divisibility by 2, 3, 5, 7 (since the square root of 97 is about 9.8).
Q4. How many prime numbers are there between 1 and 100?
There are 25 prime numbers between 1 and 100. They 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.
Q5. What are twin primes?
Twin primes are pairs of prime numbers that differ by exactly 2. Examples: (3,5), (11,13), (17,19), (29,31), (41,43), (59,61), (71,73).
Q6. Is 91 a prime number?
No, 91 is not prime. It equals 7 x 13. This is a common mistake because 91 looks prime at first glance.
Q7. Can every even number be written as a sum of two primes?
This is called Goldbach's Conjecture. It has been verified for all even numbers up to very large values, but has not been mathematically proven for all numbers. For Class 4, you can verify it for small even numbers.
Q8. What is the Sieve of Eratosthenes?
It is a method to find all primes up to a given number. Write numbers 1 to 100 in a grid, then cross out multiples of 2, 3, 5, and 7 (keeping these primes). The remaining uncrossed numbers (except 1) are all primes.
