Steps to Finding a Prime Number

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A prime number is a number that only has two factors, which are itself and the number one. Learn about divisibility rules that help to find prime numbers with information from a standardized test prep instructor in this free video on math and education.

Part of the Video Series: Math & English Education
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Video Transcript

Let's look at how to find a prime number. So first of all a prime number is a number such as 17 that has only two factors, 1 and itself. Factors means the numbers that could be multiplied to get 17. Like the number 36 has lots of factors, there's lots of pairs of numbers that multiply to be 36; 1 times 36, 2 times 18, 6 times 6, that's not prime. Seventeen is a prime number because it only has two factors, the only numbers that multiply to be 17, 1 time 17, there's no other whole numbers. By the way we're talking about whole numbers, of course 8 1/2 times 2 is 17, but we're only talking about integers, or numbers without a decimal part. So if you want to find out if a number is prime, there's a couple of ways to do it. I mean first of all, you could just look on the Internet and Google prime numbers and get an expansive list and see if it's there, but if you don't want to do that, here's a nice little trick. Lets say you're analyzing a number and you want to know if certain numbers go into it, here's some divisibility rules. Okay, if the number 2 goes into a number the number will be even and it will end in an even number. Any number that ends in an even number is going to be divisible by 2, so it'll have 2 as a factor, it wouldn't be prime. Three, any number who's digits (lets see 15, 17); Any numbers who's digits, like the number 9,171, if the digits add up to a number that is divisible by 3 then that whole number is divisible by 3, like 9 plus 1 is 10 plus 7 is 17 plus 1 is 18, it's a fun little trick. The number 18, the sum of these digits is divisible by 3, 18 divided by 3 is 6, so this number is divisible by 3. Four, great trick for the number 4. If you want to know if a number, doesn't matter how big, is divisible by 4, you take the last two digits, if that number, not adding them up like we did here, just that number itself, if that number itself is divisible by 4, then the number is divisible by 4, so this huge number we know is divisible by 4 because the last two digits are. Last one, 5. Any number that ends in a 0 or a 5 is divisible by 5, like the number 980, or 7,6,2,5. Because it ends in a 0 or a 5 we know it's divisible by 5. And if some things are divisible by 2, 3, 4 or 5, it's not prime. Beyond that you can test it by dividing it on your calculator.


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