how do you figure out what prime and composite numbers are
A prime number is a number that has only 2
factors one and itself. A composite number has more than 2 factors. The number “1” is
neither a prime number nor a composite number because it has only 1 factor.
To figure out whether a number is prime or composite, you can follow these steps:
1. Understand the definitions:
- Prime numbers are numbers that are only divisible by 1 and themselves. They have exactly two distinct positive divisors.
- Composite numbers are numbers that have more than two positive divisors. These numbers can be divided evenly by numbers other than 1 and themselves.
2. Start with the smallest natural number, which is 2, and begin checking numbers one by one.
3. For each number, check if it is divisible by any natural numbers between 2 and its square root (inclusive). Note that checking up to the square root is sufficient to determine divisibility.
4. If the number has no divisors other than 1 and itself, it is a prime number. Remember to exclude 1 since it is neither prime nor composite.
5. If the number has divisors other than 1 and itself, it is a composite number.
6. Continue this process for each subsequent number until you have determined whether all the numbers in question are prime or composite.
Alternatively, you can also use certain mathematical algorithms and formulas to determine prime numbers efficiently, but those are beyond the scope of this explanation.
Note: The number 1 is neither prime nor composite as it has only one positive divisor, which is 1.