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### Course: Math (NSDC) - English>Unit 5

Lesson 1: Factors and multiples

# 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?
• 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...).
• 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?
• 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.
• 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. . .
• 1 is neither prime nor composite.
• Wouldn't 1 be a prime number because 1 is divisible by 1 and itself?
• Each prime number has two divisors - 1 and itself. Since 1 only has one divisor, it can't be a prime.

Hope this helps!
• Is 1 the only number that is not prime or compisite? If it is what about infinity is that also not prime and compisite
• 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.
• Are negative numbers prime, composite, or neither, and can you please explain why?
• acording to my resercah, negative numbers are not prime because they are not postive intergers
• Is the number 1 a prime, composite, or neutral?
• 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.
• Why can't negative numbers be prime?
• 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?
• So Technically is -2,-3,etc a prime number
• 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.
Btw only whole numbers greater than `1` are considered in the prime/composite categories.