The smallest prime number is:
2
Understanding Prime Numbers
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Identifying the Smallest Prime Number
Let's examine the small natural numbers to see which ones fit the definition of a prime number:
- Number 1: The definition of a prime number states it must be greater than 1. So, 1 is not a prime number.
- Number 2: The divisors of 2 are 1 and 2. The only positive divisors are 1 and itself. It is also greater than 1. Therefore, 2 is a prime number.
- Number 3: The divisors of 3 are 1 and 3. The only positive divisors are 1 and itself. It is also greater than 1. Therefore, 3 is a prime number.
- Number 4: The divisors of 4 are 1, 2, and 4. It has a divisor (2) other than 1 and itself. Therefore, 4 is not a prime number.
- Number 6: The divisors of 6 are 1, 2, 3, and 6. It has divisors (2 and 3) other than 1 and itself. Therefore, 6 is not a prime number.
Comparing the numbers that are prime (2, 3, 5, etc.), the smallest one is 2.
Checking the Options
Let's look at the given options:
- 6: Not a prime number (divisible by 2 and 3).
- 2: Is a prime number (only divisible by 1 and 2).
- 1: Not a prime number (by definition, must be > 1).
- 4: Not a prime number (divisible by 2).
Based on the definition and analysis, the smallest prime number is 2.
Important Questions from Multiples and Factors
Express 486 as a product of powers of prime factors.
Let p, q, r and s be positive natural numbers having three exact factors including 1 and the number itself. If q > p and both are two-digit numbers, and r > s and both are one-digit numbers, then the value of the expression \(\frac{p-q-1}{r-s}\) is:
Find the greatest three-digit number which is a multiple of 8.
The sum of three consecutive multiples of 7 is 840. The smallest of these multiples is:
The least perfect square which is divisible by 3, 4, 5, 6, 8 is:
