# Video: The Definition of a Prime Number

What is a prime number?

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### Video Transcript

What is a prime number?

By definition, a prime number is a natural number greater than one that cannot be formed by multiplying two smaller natural numbers. First of all, a natural number are in counting numbers: one, two, three, four, five, and so on. So a prime number is a natural number that’s greater than one. So, so far, we can already eliminate one.

So already, it’s numbers such as two, three, four, five, and so on that cannot be formed by multiplying two smaller natural numbers. So if we can’t multiply two natural numbers together to get this kind of number, then this means that these numbers can’t go into it.

So we could rewrite this as: instead of focusing on what can’t multiply to get a prime number, we can focus on what you can divide to get the prime number. So a prime number is only divisible by itself. So only itself can go into it. And the only other number that could possibly go into it would be the number one because it goes into all numbers or natural numbers.

So one more way to kinda make this sound a little fancier would be instead of saying it’s only divisible by itself and one, when a number is divisible by something that means that has some factors. Factors multiply to be a number. And the only factors that a prime number could have that multiply to be itself would be itself and one.

Therefore, we can say that a prime number is a number with exactly two factors: one and itself.