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Prime Factors, HCF and LCM

Prime Numbers

A number p is a prime if it has exactly two factors; namely 1 and p. In other words, the only factors of a prime are the trivial factor and the improper factor.

A number that has a nontrivial proper factor is said to be composite.

The number 1, therefore, is neither a prime nor a composite. All other numbers which are not prime are composite. The number 2 is the smallest prime.

Examples

6 is composite, as 6 = 2×3. The numbers 2 and 3 are non-trivial proper factors of 6.

The numbers 2, 3, 5 and 7 are prime.

Let's look at a good method for discovering small primes:

Eratosthenes’s Sieve Method

Suppose we are trying to discover all prime numbers ≤ M.

1. Set the first sieve prime = 2.
2. Cross out all multiples of the current sieve prime.
3. Look for the next larger, not crossed-out number. It will become the new sieve prime.
4. Repeat this process from 2. as long as the sieve prime is not larger that the square root of M.

We demonstrate the process with numbers less than 50.

Exercise

First 100 Primes

<< Factors and Multiples | HCF and LCM Index | Prime Factorization >>