# Dividing numbers: long division with remainders | Arithmetic | Khan Academy

It never hurts to get a lot of
practice, so in this video I’m just going to do a bunch more
of essentially, what we call long division problems. And so if you have
4 goes into 2,292. And I don’t know exactly why
they call it long division, and we saw this in the
last video a little bit. I didn’t call it long division
then, but I think the reason why is it takes you a long
time or it takes a long piece of your paper. As you go along, you kind of
have this thing, this long tail that develops on the problem. So all of those are, at least,
reasons in my head why it’s called long division. But we saw in the last video
there’s a way to tackle any division problem while just
knowing your multiplication tables up to maybe 10
times 10 or 12 times 12. But just as a bit of review,
this is the same thing as 2,292 divided by 4. And it’s actually the same
thing, and you probably haven’t seen this notation before,
as 2,292 divided by 4. This, this, and this are
all equivalent statements on some level. And you could say, hey Sal,
that looks like a fraction in case you have seen
fractions already. And that is exactly what it is. It is a fraction. But anyway, I’ll just focus on
this format and in future videos we’ll think about other
ways to represent division. So let’s do this problem. So 4 goes into 2
how many times? It goes into 2 no times,
so let’s move on to– let me just switch colors. So let’s move on to the 22. 4 goes into 22 how many times? Let’s see. 4 times 5 is equal to 20. 4 times 6 is equal to 24. So 6 is too much. So 4 goes into 22 five times. 5 times 4 is 20. There’s going to be a
little bit of a leftover. And then we subtract
22 minus 20. Well that’s just 2. And then you bring down this 9. And you saw in the last video
exactly what this means. When you wrote this 5 up
here– notice we wrote in the 100’s place. So this is really a 500. But in this video I’m just
going to focus more on the process, and you can think more
about what it actually means in terms of where I’m
writing the numbers. But I think the process
is going to be crystal clear hopefully, by
the end of this video. So we brought down the 9. 4 goes into 29 how many times? It goes into at
least six times. What’s 4 times 7? 4 times 7 is 28. So it goes into it at
least seven times. What’s 4 times 8? 4 times 8 is 32, so it can’t go
into it eight times so it’s going to go into it seven. 4 goes into 29
nine seven times. 7 times 4 is 28. 29 minus 28 to get our
remainder for this step in the problem is 1. And now we’re going to
bring down this 2. We’re going to bring it
down and you get a 12. 4 goes into 12? That’s easy. 4 times 3 is 12. 4 goes into 12 three times. 3 times 4 is 12. 12 minus 12 is 0. We have no remainder. So 4 goes into 2,292
exactly 573 times. So this 2,292 divided by 4
we can say is equal to 573. Or we could say that this thing
right here is equal to 573. Let’s do a couple of more. Let’s do a few more problems. So I’ll do that red color. Let’s say we had 7
going into 6,475. Maybe it’s called long division
because you write it nice and long up here and you
have this line. I don’t know. There’s multiple reasons why it
could be called long division. So you say 7 goes
into 6 zero times. So we need to keep
moving forward. So then we go to 64. 7 goes into 64 how many times? Let’s see. 7 times 7 is? Well, that’s way too small. Let me think about
it a little bit. Well 7 times 9 is 63. That’s pretty close. And then 6 times 10 is
going to be too big. 7 times 10 is 70. So that’s too big. So 7 goes into 64 nine times. 9 times 7 is 63. 64 minus 63 to get our
remainder of this stage 1. Bring down the 7. 7 goes into 17 how many times? Well, 7 times 2 is 14. And then 7 times 3 is 21. So 3 is too big. So 7 goes into 17 two times. 2 times 7 is 14. 17 minus 14 is 3. And now we bring down the 5. And 7 goes into 35? That’s in our 7 multiplication
tables, five times. 5 times 7 is 35. And there you go. So the remainder is zero. So all the examples I did
so far had no remainders. Let’s do one that maybe
might have a remainder. And to ensure it has a
remainder I’ll just make up the problem. It’s much easier to make
problems that have remainders than the ones that
don’t have remainders. So let’s say I want to divide 3
into– I’m going to divide it into, let’s say 1,735,092. This will be a nice,
beastly problem. So if we can do this we
can handle everything. So it’s 1,735,092. That’s what we’re
dividing 3 into. And actually, I’m not sure if
this will have a remainder. In the future video I’ll show
you how to figure out whether something is divisible by 3. Actually, we can
do it right now. We can just add up
all these digits. 1 plus 7 is 8. 8 plus 3 is 11. 11 5 five is 16. 16 plus 9 is 25. 25 plus 2 is 27. So actually, this number
is divisible by 3. So if you add up all of
the digits, you get 27. And then you can add up those
digits– 2 plus 7 is 9. So that is divisible by 9. That’s a trick that
only works for 3. So this number actually
is divisible by 3. So let me change it a
little bit, so it’s not divisible by 3. Let me make this into a 1. Now this number will
not be divisible by 3. I definitely want a
number where I’ll end up with a remainder. Just so you see what
it looks like. So let’s do this one. 3 goes into 1 zero times. So we can just move forward. You could write a 0 here and
multiply that out, but that just makes it a little
bit messy in my head. So we just move
one to the right. 3 goes into 17 how many times? Well, 3 times 5 is equal to 15. And 3 times 6 is equal to
18 and that’s too big. So 3 goes into 17 right
here five times. 5 times 3 is 15. And we subtract. 17 minus 15 is 2. And now we bring down this 3. 3 goes into 23 how many times? Well, 3 times 7 is equal to 21. And 3 times 8 is too big. That’s equal to 24. So 3 goes into 23 seven times. 7 times 3 is 21. Then we subtract. 23 minus 21 is 2. Now we bring down
the next number. We bring down the 5. I think you can appreciate why
it’s called long division now. We bring down this 5. 3 goes into 25 how many times? Well, 3 times 8 gets you pretty
close and 3 times 9 is too big. So it goes into it eight times. 8 times 3 is 24. I’m going to run out of space. You subtract, you get 1. 25 minus 24 is 1. Now we can bring down this 0. And you get 3 goes into
10 how many times? That’s easy. It goes into it three times. 3 times 3 is 9. That’s about as close
to 10 as we can get. 3 times 3 is 9. 10 minus 9, I’m going to
have to scroll up and down here a little bit. 10 minus 9 is 1, and then we
can bring down the next number. I’m running out of colors. I can bring down that 9. 3 goes into 19 how many times? Well, 6 is about as
close as we can get. That gets us to 18. 3 goes into 19 six times. 6 times 3– let me scroll down. 6 times 3 is 18. 19 minus 18– we subtract
it up here too. 19 minus 18 is 1 and
then we’re almost done. I can revert back to the pink. We bring down this
1 right there. 3 goes into 11 how many times? Well, that’s three times
because 3 times 4 is too big. 3 times 4 is 12, so
that’s too big. So it goes into it three times. So 3 goes into 11 three times. 3 times 3 is 9. And then we subtract
and we get a 2. And there’s nothing
left to bring down. When we look up here there’s
nothing left to bring down, so we’re done. So we’re left with the
remainder of 2 after doing this entire problem. So the answer, 3 goes into
1,735,091– it goes into it 578,363 remainder 2. And that remainder 2 was what
we got all the way down there. So hopefully you now appreciate
and you can tackle pretty much any division problem. And you also, through this
exercise, can appreciate why it’s called long division.

## 100 thoughts on “Dividing numbers: long division with remainders | Arithmetic | Khan Academy”

1. Jan Shukoor says:

Thanks so much now i dont have any mistakes on my homeworks or qwiz

2. Jan Shukoor says:

¡

3. Ola Saeed says:

what do i do with th remainder >?!!! how do i change it to decimal
?

4. Jessey Kollie says:

Awsomeness!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!:)

5. Jeandra Rodriguez says:

6. QuackyFlounder says:

This literally teached me how to divide

7. QuackyFlounder says:

Tks

8. Fresh Af says:

Dumb shit

9. Frosty says:

now this teach me a lot about division
Thank you mr.Khan

10. N. Corman says:

Dude, You're the best…..Thank you for teaching me & other youtubers. God bless!

11. TheHappyGamer -Gaming and More! says:

12. Carlo Cinco says:

13. Carlo Cinco says:

this help me alot

14. Kiarra Deloatch says:

your the only video I'm going to thanks your the best Mr.khan

15. Izma Haider says:

thank you

16. Bana Hussien says:

i didnt understand it but now perfect thanx mrs.khan !

17. Blossom Vlogs says:

me to i had it for home
work

My teacher told me to watch this soooo ok what the heck it taught me alot thanks

19. SuperiorYT says:

( ͡° ͜ʖ ͡°) very helpful! Thx a lot!

20. Al Suarez says:

thx alot mr.knan! this helped me alot! A+ on my test because of you!

21. Mohammed Mannan says:

thanking you for your great help'"

22. Anne Handoko says:

yo so cool

23. s says:

Omg thx so much for doing this video ! Now I understand ! And I was scared to tell my teacher I needed help but u saved my life thx SO MUCH ! 😊✨

24. minerva irizarry says:

poooooòoooooop💩💩💩💩💩💩💩😱😱😅😅😅😅

25. minerva irizarry says:

I got 100 on my test thank you☺😊😀😁😂😃😄😅😆😇😈😉😯😑😕😠😬😡😢😴😮😣😤😠😬😡😢😢😴😴😮😣😤😥😦😧😨😨😩😰😰😟😱😲😍😳😒😵😞😶😷😚😛😘😜😙😝😗😋

26. miss beauty was here says:

He's really good 😌😊🙂😜🤗😍😄😎🤓🌍💕💞😀😂😅😉🙃😌😗😜🤑🤗😐🙄😬😃😆😊☺️😍😙😝🤓😏😑🤔😁😄😇🙂😋😘😚😛😎😶😒

27. Jenifer Loja says:

can you help me

28. Denia Acosta says:

Thanks ….

29. Marie Alsaint says:

thank you because i,m the smartest person in my classroom

30. Rowan Pearson says:

that was as clear as mud

31. Nerdy Navi says:

Tysm! This helped me a lot, but can you make a video on how to present the remainder as a decimal? If you have already can someone link me the video..

32. Omit family says:

im the smartest kid in the world

33. Cristina Lucero says:

this guy is good and it helped me a lot

34. StrikezoneDD says:

what did you do to get the colors

35. Froilan Reyes says:

i have the app

36. Simon Jeppesen says:

Why don't they teach why you pull down the numbers instead of just giving you a rule to by. Noone learns anything from that…

37. Ryan Hvizda says:

Thanks

38. Ryan Hvizda says:

they call it long division because it is a another to say big

39. someone unknown says:

Panga Chonga

40. Akira Gamer Girl says:

Thank you because now i know how to divide with remainder😀😀😀😀

41. Celia Cordtz says:

thanks for helping me.

he sounds like a murderer when he speaks

43. Maxwell Oneill says:

nooooooooooooooooooooooooooooooooooooooooo

44. Maxwell Oneill says:

this sucks

45. Maxwell Oneill says:

i kid

46. Fitnat Cheikh Ghazal says:

U ARE AMAZING TYSM!!!!! I DID NOT UNDERSTAND LONG DIVISION UNTIL NOW!! I USED TO GET D'S!! TYSM

47. Ebube Nwogbo says:

good

48. Flower Girl says:

thanks i needed this im doing math pssa's and i forgot how to do long division

49. Jenny Benito says:

great know i no how😉☺👼👌👍✌👏

50. Moms Spaghetti says:

Its funny how you learn a bit of this during grade 4 math class then it comes back at highschool, being more complicated

51. WOLTHIGAMEZMC says:

thank you

52. The1SkullRider says:

What is this????

53. The1SkullRider says:

I suck at dis

54. The1SkullRider says:

Thank u

55. The1SkullRider says:

This is gross I'm to smart 4 this crap

56. manaal syed says:

57. Sasha Bailey says:

This helped so much, I totally had that moment of, "OMG, I get it!

58. Karen Ruiz says:

This really helped my class

59. Steampunk Steven says:

In the video it’s so easy but when you try this in school it’s so hard. But anyways thanks a lot khan

60. Sebastian DONALD-BROOKS says:

booooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

61. Khuyen Jennifer says:

62. Alisya Thahira says:

Lol my math online course told me to watch this xD

63. kai loft says:

what do you use for that

64. Dixe Ann Hutchinson says:

I am so happy I watched this because now I am going to college because of you 😊😊😊😊

65. alice p says:

i need help with division with 4 or more dividends! help!!!!!!!!

66. Yareli Pierre says:

great

67. ZyZy !! says:

You explain stuff way better then my teacher. Whenever I need help with math I just look at your videos and it all makes sense.

68. Brandon Yih says:

helping so much for homework!

69. Faznarazeen Razeen nana says:

This is amazing my forth grader learned a lot for her exam from your channel.

70. Runch Randa Dimples says:

I love this guy's work!

71. Rose Smith says:

i will pass the fsa test

72. Gacha Fandom says:

thanks for explaining this helped me in my test Mr.khan

73. Fatemah Lugbi says:

Does 4 go into 4?😊

74. кяisтеа uwu says:

Ok

thank you this really helped me keep doing what you do

76. Taylor Wells says:

Is the remainder 2 a point 2 at the end????? Thats what Im trying to figure out. Is the answer 578363.2?

77. Friskee Fi says:

I am terrible at Multu-digit division

78. Jonathan Quirke says:

You’re so smart

79. Jonathan Quirke says:

You’re so smart #sosmart keep it up dude

80. Jonathan Quirke says:

Do you think he’s smart like if you agree

81. negralinnda says:

82. CHEEZ WHIz FORTNITE CHEEZ WHIz FORTNITE says:

Thank you my teacher makes me watch you in school

83. Shalett Smallwood says:

All I learnd is he likes colers

84. Maliya P-Louis says:

Or LONG DIVISION BEACUSE THE NUMBER is LONG ps THXXXXXXXXX (thx means thank you) you helped me with my homworkkkkkkkk😃😃I watch you in class on computer

85. Diana Botello says:

thank you for the video! My students were very entertained; however, you changed the division between frames 6:36 and 6:42–which confused them greatly and made the difference between the remainder and no remainder =)

86. thatshaps says:

this really helped me i followed it step by step doing my math sheets and i got the right awnsers every time 🙂

87. Kate Becker says:

Umm who else listened to this in 4th grade

88. Craig Richardson says:

Thanks Khan Academy you've helped me out a lot over the years

89. Courtney Reyes says:

THANK YOU MY KID GETS IT SO MUCH THANK YOU YOUR THE BEST

90. Tracey S says:

Thanks I needed this

Yay I learned to edit

91. Lonely Patato says:

Thanks sooooooo much!

92. Patience Gasu says:

Thanks u so much for helping to solved this problem 😊

thanks for helping me i was scared to ask much teacher you a life saver Khans academy 🙂

94. Asteelo paparazzi says:

1:12 It does bloody look like a fraction though, but I've never seen a fraction that big so I dont know!

95. Asteelo paparazzi says:

6:15 Why did he just skip zero!?

96. Who Knows says:

Every example being a single digit number limits the helpfulness of this. It's like every math lesson ever uses the simplest examples. Single digits, 10's, 100's, 2's or 5's. ect.

97. kemi ogunmola says:

Ok it kinda of help me😐😮 but the million was not understandable can you explain it more please😭😨😰😔.

98. Kiran Bahirwani says:

Thank you

99. Aijia Renee says:

This is easy