Finding the Primary Numbers: Tips and Tricks for Math Students

How to Find the Primary Numbers

Primary numbers are usually called prime numbers. They are numbers that are only divisible by two numbers: themselves and one. Two, 13 and 17 are all examples of prime numbers. Composite numbers are the opposite of prime numbers. They can be divided by themselves, one and at least one other number. For instance, 25 is a composite number because it is divisible by three numbers: one, five and 25.

Finding Prime Numbers: Tip #1

Any even number greater than two cannot be prime. This is true because even numbers are always divisible by two. As a result, it is always divisible by another number besides just itself and one. For example, we know that the number eight is divisible by itself and one. Since it's even, we also know it's divisible by two. That means it can be evenly divided by at least three numbers, so it can't be prime.

Example

Let's try this trick with a larger number, like 472. It's an even number because its last digit is two, so it's not prime. We don't have to bother finding out what other numbers 472 is divisible by, because we already know that it can be divided by itself, one and two. This is all the information we need to determine that 472 isn't a prime number.

Remember that if a number is not even, this does not automatically make it a prime number. For example, the number 15 isn't even, but it isn't prime, either. It isn't divisible by two, but it is divisible by one, itself, three and five.

Finding Prime Numbers: Tip #2

If a number isn't even, then you can't apply tip number one to find out if it's prime. For odd numbers larger than three, here's another trick you can use: Add together all of the number's digits, and try to divide them by three. If the summed-up digits can be divided evenly by three, then the original number is divisible by three, so it's not prime.

Example

If you add up the digits of the number 21, two and one, you get three. Three is evenly divisible by three, so now you know that 21 is divisible by three, one and itself. This means that it's not prime. We can use the same trick on the number 57. The sum of five and seven is 12, and 12 is divisible by three. This means that 57 is also divisible by three, one and itself, so it isn't prime.

As with tip number one, remember that just because you find out a number isn't divisible by two or three, this doesn't mean it's prime. It could still be divisible by other numbers, like five or seven.

Finding Prime Numbers: Tip #3

The tricks described in tips one and two are called divisibility rules, and there are rules like them for all of the single-digit numbers. If you find that a number isn't divisible by two, three, five or seven, then it is safe to say that it's prime. You don't need to apply the divisibility rules for four, six, eight or nine, because if you've already determined that the number isn't divisible by two or three, then it can't be divisible by these numbers. Here are the divisibility rules for five and seven:

A number that ends in a zero or a five isn't prime, because it's divisible by five.

Example: The number 500,125 ends in a five, so it's divisible by five. This means it's not prime because it's divisible by at least three numbers: itself, one and five.

If a number's last digit doubled and subtracted from the remaining part of the number produces an answer that is either zero or divisible by seven, then it's not prime, because it's divisible by seven.

Example: The number 511 can't be prime because if you multiply the last digit by two (1 x 2), and subtract the result from 51 (51 - 2), you get 49. The number 49 is divisible by seven, so 511 can be divided by seven, as well as itself and one.

Just like the divisibility rules for two and three, which only work for numbers greater than two and three, the divisibility rules for five and seven only work for numbers greater than five and seven. Two, three, five and seven are all prime numbers, because they're only divisible by themselves and one.