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## Pre-algebra

### Course: Pre-algebra > Unit 1

Lesson 2: Prime and composite numbers# Recognizing prime and composite numbers

Can you recognize the prime numbers in this group of numbers? Which are prime, composite, or neither? Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- Is infinity a prime number?(143 votes)
- A number must be a "natural number" for it to be prime and infinity is not a natural number. Natural numbers are positive integers (1,2,3,4,5,etc...).(145 votes)

- How is 17 not divisible by 2, 3, 4, 5, 6, and so on? because 5 / 17, 4 / 17 and so on still has an answer to it so how is it not divisible? and even more numbers like other prime numbers?(20 votes)
- When you are looking for divisibility, you are trying to see if a number is divided by another number, the result is a whole number. For example, 15/3 is 5, and 5 is a whole number, so 15 is divisible by 3. However, if you do 15/4, your answer is 3.75 or 3 3/4, which is not a whole number.(11 votes)

- I really dont quite get this, 1 isn't a prime number, is it? I looked it up and it didn't show 1 as an example for a prime number, or composite. . .(16 votes)
- 1 is neither prime nor composite.(5 votes)

- Wouldn't 1 be a prime number because 1 is divisible by 1 and itself?(9 votes)
- Each
**prime number**has two divisors - 1 and itself. Since 1 only has one divisor, it can't be a prime.

Hope this helps!(8 votes)

- Is 1 the only number that is not prime or compisite? If it is what about infinity is that also not prime and compisite(3 votes)
- In the Halls of the Khan Academy, under the sections Math, Pre-Algebra, Factors and Multiples, in the lecture, "Prime and composite numbers intro", section, "The number 1";

The only factor of 1 is 1.

A prime number has exactly two factors so 1 isn't prime.

A composite number has more than 2 factors, so 1 isn't composite.

And what about infinity, as pointed out by CarlBiologist in the Q&A section of the video, Recognizing prime and composite numbers;

"A number must be a "natural number" for it to be prime and infinity is not a natural number. Natural numbers are positive integers (1,2,3,4,5,etc...)."

But even more so, as I recently learned, infinities are usually referred to as the "limit of functions" and not as a "value" or an arbitrarily large number, so not prime or composite.(8 votes)

- Is the number 1 a prime, composite, or neutral?(3 votes)
- It is neither. A prime number has to have only two factors: 1 and itself. 1 only has one factor (itself) so it is, as you were saying, neutral.(5 votes)

- Are negative numbers prime, composite, or neither, and can you please explain why?(4 votes)
- acording to my resercah, negative numbers are not prime because they are not postive intergers(3 votes)

- Why can't negative numbers be prime?(2 votes)
- Following this logic, if prime numbers cannot be products of their own negative factors, no numbers are prime using the 'exactly 2 factors' rule. For example 5 is a product of 1 & 5 AND -1 & -5. Therefore it has 4 factors, not 2. If we specify that factors must be positive this would remove negative numbers from the list of prime numbers, but this then seems like we're making rules to fit. Why do prime numbers have to be positive?(2 votes)

- So Technically is -2,-3,etc a prime number(3 votes)
- Technically no.

Prime numbers have exactly 2 factors: the number and 1

-2 has 4 factors: -1(2) and -2(1)

-3 would also have 4 factors.

Hope this helps.(5 votes)

- Is 10 a prime number?(3 votes)
- You can be pretty certain that 10 is not a prime number. Any even value, except 2, will be composite because it has at least three factors: 1, itself, and 2, the "half". So one of the first requirements we need for the value is to be an odd number (so it is
*not divisible by 2*). However, this does not guarantee all odd numbers to be prime, either. Values that**end in 5**(except 5 itself) are composite because they have at least 1, itself, and 5 for a minimum of three factors. Multiples of 3, like 9 and 27, will be divisible by 1, itself, and 3 for a minimum of three factors.(3 votes)

## Video transcript

Determine whether the following
numbers are prime, composite, or neither. So just as a bit of
review, a prime number is a natural number-- so one of
the counting numbers, 1, 2, 3, 4, 5, 6, so on and so forth--
that has exactly two factors. So its factors are 1 and itself. So an example of a
prime factor is 3. There's only two
natural numbers that are divisible into 3-- 1 and 3. Or another way to think about
it is, the only way to get 3 as a product of other
natural numbers is 1 times 3. So it only has 1 and itself. A composite number
is a natural number that has more than just
1 and itself as factors. And we'll see examples of
that and neither-- we'll see an interesting case
of that in this problem. So first let's think about 24. So let's think
about all of the-- I guess you could think of
it as the natural numbers or the whole numbers,
although 0 is also included in whole numbers. Let's think of all of the
natural counting numbers that we can actually
divide into 24 without having any remainder. We'd consider those the factors. Well, clearly it is
divisible by 1 and 24. In fact, 1 times
24 is equal to 24. But it's also divisible by 2. 2 times 12 is 24. So it's also divisible by 12. And it is also divisible by 3. 3 times 8 is also equal to 24. And even at this point,
we don't actually have to find all of the factors
to realize that it's not prime. It clearly has more factors
than just 1 and itself. So then it is clearly
going to be composite. This is going to be composite. Now, let's just finish factoring
it just since we started it. It's also divisible by 4. And 4 times 6-- had just
enough space to do that. 4 times 6 is also 24. So these are all of the
factors of 24, clearly more than just one and 24. Now let's think about 2. Well, the non-zero whole numbers
that are divisible into 2, well, 1 times 2
definitely works, 1 and 2. But there really
aren't any others that are divisible into 2. And so it only has two
factors, 1 and itself, and that's the definition
of a prime number. So 2 is prime. And 2 is interesting because it
is the only even prime number. And that might be
common sense you. Because by definition, an
even number is divisible by 2. So 2 is clearly divisible by 2. That's what makes it even. But it's only
divisible by 2 and 1. So that's what makes it prime. But anything else
that's even is going to be divisible by
1, itself, and 2. Any other number
that is even is going to be divisible by
1, itself, and 2. So by definition,
it's going to have 1 and itself and something else. So it's going to be composite. So 2 is prime. Every other even number
other than 2 is composite. Now, here is an
interesting case. 1-- 1 is only divisible by 1. So it is not prime,
technically, because it only has 1 as a factor. It does not have two factors. 1 is itself. But in order to
be prime, you have to have exactly two factors. 1 has only one factor. In order to be
composite, you have to have more than two factors. You have to have 1, yourself,
and some other things. So it's not composite. So 1 is neither
prime nor composite. And then finally we get to 17. 17 Is divisible by 1 and 17. It's not divisible by 2,
not divisible by 3, 4, 5, 6. 7, 8, 9 10, 11, 12,
13, 14, 15, or 16. So it has exactly two
factors-- 1 and itself. So 17 is once
again-- 17 is prime.