Recognizing prime and composite numbers | Factors and multiples | Pre-Algebra | Khan Academy

Recognizing prime and composite numbers | Factors and multiples | Pre-Algebra | Khan Academy


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.

50 thoughts on “Recognizing prime and composite numbers | Factors and multiples | Pre-Algebra | Khan Academy

  • July 18, 2011 at 4:28 pm
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    yay first viewer πŸ˜€ but you guys r great ive learned alot from your lessons keep it up πŸ˜€

    Reply
  • April 4, 2012 at 5:02 pm
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    how.. are you so smart?

    Reply
  • April 5, 2012 at 4:13 pm
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    nice πŸ˜€

    Reply
  • July 17, 2012 at 11:45 pm
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    { so smart}

    Reply
  • March 5, 2013 at 11:34 pm
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    I like the way you repeat certain words and sentences when you write. somehow it helps memorizing things

    Reply
  • September 8, 2013 at 10:33 pm
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    this is awesome (except i'm watching this for school

    Reply
  • October 4, 2013 at 1:44 am
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    hi

    Reply
  • October 26, 2013 at 7:21 pm
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    I just have to say that I just love your videos! I'm teaching 6th grade math this year and you have helped me so much.

    Reply
  • October 29, 2013 at 11:44 am
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    You could argue it's neither, it's composite 0/x is 0 but it cannot be divided by itself so a different kind of neither to 1.

    Reply
  • April 23, 2014 at 8:33 pm
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    What is an "un-natural" number?

    Reply
  • October 17, 2014 at 1:26 am
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    is 325 prime or composite?

    Reply
  • October 14, 2015 at 12:49 am
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    He's better at teaching than my real teacher😢

    Reply
  • October 20, 2015 at 10:44 pm
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    I have a problem, They never let me do anything like 2 24 72 1 34 ect, they threw me straight into 179 734 ect its ridiculous.

    Reply
  • December 7, 2015 at 2:01 pm
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    thank you. . .
    U

    Reply
  • January 7, 2016 at 1:35 am
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    I'm your student Mia you may not remember me . Waaaaaaaaaaaawaaaaaaaawaaaaaaaawaaaaawaaaaa !!!!!!!!!!!!!!!! 😭😒πŸ˜₯

    Reply
  • January 14, 2016 at 11:17 pm
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    I am your student but I still need help with prime numbers

    Reply
  • March 15, 2016 at 6:22 pm
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    AwesomeπŸ˜€πŸ˜‚πŸ˜†

    Reply
  • March 15, 2016 at 6:27 pm
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    VERY clearly explained

    Reply
  • April 28, 2016 at 11:45 pm
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    is this for grade 4

    Reply
  • June 16, 2016 at 12:06 am
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    Thank you u helped with my finals

    Reply
  • July 1, 2016 at 9:14 pm
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    Omg thanks we barely covered prime and composite

    Reply
  • September 5, 2016 at 5:10 pm
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    i need more examples on composite number.
    basically the difference between prime number and composite number.

    Reply
  • September 21, 2016 at 1:18 am
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    hi

    Reply
  • November 8, 2016 at 11:24 pm
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    thanks i have a test on this tomorrow

    Reply
  • December 5, 2016 at 5:56 pm
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    This helps a lot.

    Reply
  • January 17, 2017 at 11:58 pm
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    What grade is this for?

    Reply
  • January 24, 2017 at 8:10 pm
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    4th grade

    Reply
  • January 26, 2017 at 7:11 pm
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    im 23 and i never understood this now i do thank you

    Reply
  • May 29, 2017 at 11:03 pm
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    THANK YOU!!!

    Reply
  • June 8, 2017 at 8:51 am
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    This video has a caption of over 30 languages. SiCK!

    Reply
  • October 18, 2017 at 10:09 pm
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    thank you do much this is going to help SOOO much

    Reply
  • November 20, 2017 at 12:52 pm
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    All thanks to Sal Khan! thank u soooo much

    Reply
  • November 22, 2017 at 3:30 am
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    Thanks I needed to learn that

    Reply
  • January 6, 2018 at 9:23 am
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    please check 13233435631 is a composite number

    Reply
  • January 28, 2018 at 10:14 pm
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    Gang gang

    Reply
  • February 1, 2018 at 5:54 am
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    So tu tu

    Reply
  • February 24, 2018 at 6:12 pm
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    you said a prime is one itself how 59 is a prime number?

    Reply
  • March 5, 2018 at 5:32 pm
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    Musalman murdabad

    Reply
  • March 15, 2018 at 9:03 am
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    You can get the same as the same as the same as the same as the same as last year we had a chance to see if it is not

    Reply
  • June 21, 2018 at 5:21 pm
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    Thanks sir

    Reply
  • September 6, 2018 at 5:21 pm
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    Thank you again.

    Reply
  • September 25, 2018 at 1:01 am
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    >β€’< mewo

    Reply
  • October 22, 2018 at 8:02 pm
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    It’s good practice, thanks

    Reply
  • January 31, 2019 at 2:06 am
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    These Khan math videos are on POINT! learning more here than from the instructor

    Reply
  • May 6, 2019 at 12:18 am
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    2019 anyone?

    Reply
  • July 22, 2019 at 8:32 pm
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    This really helped !!

    Reply
  • August 1, 2019 at 10:56 pm
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    I watched on 5 other videos this ones the best

    Reply
  • August 15, 2019 at 5:46 pm
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    I clicked on this bc it helps me understand better than my homeschool vids

    Reply
  • September 22, 2019 at 5:37 am
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    w Learning thia at school πŸ™

    Reply

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