How to Identify Prime and Composite Numbers

TenMarks teaches you how to identify if a number is prime, composite, or neither.

How to Identify Prime and Composite Numbers Learn how to identify if a number is prime or composite or neither, so we’re given four particular numbers, 2, 6, 48 and 0 and we have to determine whether they’re prime or composite okay, so what are the rules? Well we know that if a number is a prime number, its factors will be 1 and itself. It will only have 2 factors; if a number is composite it will have greater than 2 factors. So let’s do this, the first number is 2, well let’s write the factors of 2, the factors of 2 are 1 and 2, that’s the only way to do it. Because it has 2 factors, number of factors is 2, I know this is a prime number right? So 2 become a prime number, now lets look at the number 6. Well 6, lets do the factors of 6; factors of 6 are 1×6 or 1×2×3 because 6 can be broken down into 2×3 which is the number of factors is 3 which means this is a composite number because it's got more than 2 factors, so this is a composite number. Now lets look at the third one which is 48, the factors of 48 are 1×48 or 1×2×24, I can write 24 as 2×12 which can also be written as 12 can be written as 3×4, you got the idea. So now I can write this as 1×2×2×3×2×2, so I have 6 factors, if it's more than two factors, then it's a composite number so I know 48 is a composite number as well. Last is the number 0, now 0 is a unique number because it has an infinite number of factors, let me teach you why that is. It has an infinite number of factors because anything multiplied by 0 gives you a 0, so I can write 0 down as 1×0, I can write it down as 2×0, I can write it down as 3×0, I can also write it down as 2×3×0, you get the idea. I can multiply anything as long as it's by itself the answer will be 0, so this number is neither prime nor composite. This is called an exception. Zero is neither prime nor composite, so that’s jot that down. So let’s quickly recap what we’ve learned. If a number is prime it can only have two factors which is the number 1 and itself. If a number is composite, it will have more than 2 factors, it must have more than 2 factors. If we look at the number 2 it only has two factors 1 and itself, 1 and 2. When we look at 6 and 48 they both have multiple factors more than three. 6 has three factors, 48 has six factors, so both of these are composite numbers. And the number 0 is an exception because it has an infinite number of factors hence it is neither.