The smallest prime number is 2. It is also the only even prime number — all other even numbers are divisible by 2 and hence not prime. A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself. 1 is NOT a prime number (it has only one factor).
Smallest prime number = 2.
2 is the only even prime number.
1 is NOT a prime number (it has only one factor).
Prime numbers up to 10: 2, 3, 5, 7.
There are 25 prime numbers between 1 and 100.
Fundamental Theorem of Arithmetic: every integer > 1 is prime or a product of primes.
Smallest Prime Number: 2
Why is 2 the smallest prime? • 2 has exactly two factors: 1 and 2 • It satisfies the definition of a prime number • 1 is NOT prime because it has only one factor (1) • Every number < 2 (i.e., 1) is not prime by definition
Why is 2 special? • 2 is the ONLY even prime number • Every other even number is divisible by 2, making it composite • 2 is the first prime in the list of primes
Prime Numbers 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 Total: 25 prime numbers between 1 and 100
Key Facts:
| Statement | Answer |
|---|---|
| Smallest prime number | 2 |
| Only even prime | 2 |
| Is 1 a prime? | No (only 1 factor) |
| Is 0 a prime? | No |
| Smallest odd prime | 3 |
| Largest 2-digit prime | 97 |
| Prime numbers up to 10 | 2, 3, 5, 7 |
| Twin primes | Primes differing by 2: (3,5), (5,7), (11,13) |
Properties of Prime Numbers: • Every prime > 2 is odd • 2 is the only even prime • Two consecutive numbers cannot both be prime (except 2 and 3) • Every integer > 1 is either prime or can be expressed as a product of primes (Fundamental Theorem of Arithmetic) • There are infinitely many prime numbers (proved by Euclid)
How to Check if a Number is Prime: • Trial division: check if any number from 2 to √n divides n • Example: Is 37 prime? √37 ≈ 6.1 → check 2, 3, 5 — none divide 37 → 37 is prime
The smallest prime number is 2. It is also the only even prime number — all other even numbers are divisible by 2, making them composite. 1 is not prime because it has only one factor. Prime numbers up to 10 are: 2, 3, 5, 7. There are 25 prime numbers between 1 and 100.
Euclid's Division Lemma — Statement and Examples
Learn Euclid's Division Lemma for Class 10 Maths. Statement: a = bq + r. Understand how it is used to find the HCF of two numbers with solved examples.
Evaluate 101 × 99 Using Algebraic Identity
101 × 99 = 9999. Using identity (a+b)(a-b) = a²−b²: (100+1)(100−1) = 100²−1² = 10000−1 = 9999. Step-by-step solution.
Evaluate 501 × 501 Without Actual Multiplication — Using Algebraic Identity
501 × 501 = 251001. Solve using (a+b)² = a² + 2ab + b² identity where a=500, b=1. Learn the method with more examples and FAQs.
Evaluate i^888 — Powers of i (Imaginary Number)
i^888 = 1. Since i^4 = 1, divide 888 by 4 to get remainder 0. i^888 = (i^4)^222 = 1. Learn the cyclic pattern of powers of i with examples and FAQs.
What is the Only Even Prime Number?
Learn why 2 is the only even prime number in mathematics. Understand the definition of prime numbers and why all other even numbers are composite.
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