Divisibility tests for 2, 3, 4, 5, 6, 9, 10 | Factors and multiples | Pre-Algebra | Khan Academy

Worked example of basic divisibility tests

Missed the previous lesson?

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

[matiaspereira]

The divisibility rules of all numbers from 1 to 100

1: Any number is a multiple of 1

2: The number ends in 0, 2, 4, 6 or 8

3: The sum of the digits is a multiple of 3

4: The last 2 digits are a multiple of 4; the 10s digit is even and the last digit is 0, 4 or 8, or the 10s digit is odd and the last digit is 2 or 6

5: The number ends in 0 or 5

6: The number is a multiple of 2 and 3 at the same time

7: The difference between twice the last digit and the rest of the number is 0 or a multiple of 7

8: The last 3 digits are a multiple of 8; the 100s digit is even and the last 2 digits are 00 or a multiple of 8, or the 100s digit is odd and the last 2 digits are the result of multiplying 4 by an odd number

9: The sum of the digits is a multiple of 9

10: The number ends in 0

11: The difference between the last digit and the rest of the number is 0 or a multiple of 11

12: The number is a multiple of 3 and 4 at the same time

13: The sum of 4 times the last digit and the rest of the number is a multiple of 13

14: The number is a multiple of 2 and 7 at the same time

15: The number is a multiple of 3 and 5 at the same time

16: The last 4 digits are a multiple of 16; the 1, 000s digit is even and the last 3 digits are 000 or a multiple of 16, or the 1, 000s digit is odd and the last 3 digits are the result of multiplying 8 by an odd number

17: The difference between 5 times the last digit and the rest of the number is 0 or a multiple of 17

18: The number is a multiple of 2 and 9 at the same time

19: The sum of twice the last digit and the rest of the number is a multiple of 19

20: The number ends in 00, 20, 40, 60 or 80

21: The number is a multiple of 3 and 7 at the same time

22: The number is a multiple of 2 and 11 at the same time

23: The sum of 7 times the last digit and the rest of the number is a multiple of 23

24: The number is a multiple of 3 and 8 at the same time

25: The number ends in 00, 25, 50 or 75

26: The number is a multiple of 2 and 13 at the same time

27: The difference between 8 times the last digit and the rest of the number is 0 or a multiple of 27

28: The number is a multiple of 4 and 7 at the same time

29: The sum of thrice the last digit and the rest of the number is a multiple of 29

30: The number is a multiple of 3 and 10 at the same time

31: The difference between thrice the last digit and the rest of the number is 0 or a multiple of 31

32: The last 5 digits are a multiple of 32; the 10, 000s digit is even and the last 4 digits are 0, 000 or a multiple of 32, or the 10, 000s digit is odd and the last 4 digits are the result of multiplying 16 by an odd number

33: The number is a multiple of 3 and 11 at the same time

34: The number is a multiple of 2 and 17 at the same time

35: The number is a multiple of 5 and 7 at the same time

36: The number is a multiple of 4 and 9 at the same time

37: The difference between 11 times the last digit and the rest of the number is 0 or a multiple of 37

38: The number is a multiple of 2 and 19 at the same time

39: The number is a multiple of 3 and 13 at the same time

40: The last 3 digits are a multiple of 40; the 100s digit is even and the last 2 digits are 00, 40 or 80, or the 100s digit is odd and the last 2 digits are 20 or 60

41: The difference between 4 times the last digit and the rest of the number is 0 or a multiple of 41

42: The number is a multiple of 2, 3 and 7 at the same time

43: The sum of 13 times the last digit and the rest of the number is a multiple of 43

44: The number is a multiple of 4 and 11 at the same time

45: The number is a multiple of 5 and 9 at the same time

46: The number is a multiple of 2 and 23 at the same time

47: The difference between 14 times the last digit and the rest of the number is 0 or a multiple of 47

48: The number is a multiple of 3 and 16 at the same time

49: The sum of 5 times the last digit and the rest of the number is a multiple of 49

50: The number ends in 00 or 50

51: The number is a multiple of 3 and 17 at the same time

52: The number is a multiple of 4 and 13 at the same time

53: The sum of 16 times the last digit and the rest of the number is a multiple of 53

54: The number is a multiple of 2 and 27 at the same time

55: The number is a multiple of 5 and 11 at the same time

56: The number is a multiple of 7 and 8 at the same time

57: The number is a multiple of 3 and 19 at the same time

58: The number is a multiple of 2 and 29 at the same time

59: The sum of 6 times the last digit and the rest of the number is a multiple of 59

60: The number is a multiple of 3 and 20 at the same time

61: The difference between 6 times the last digit and the rest of the number is 0 or a multiple of 61

62: The number is a multiple of 2 and 31 at the same time

63: The number is a multiple of 7 and 9 at the same time

64: The last 6 digits are a multiple of 64; the 100, 000s digit is even and the last 5 digits are 00, 000 or a multiple of 64, or the 100, 000s digit is odd and the last 5 digits are the result of multiplying 32 by an odd number

65: The number is a multiple of 5 and 13 at the same time

66: The number is a multiple of 2, 3 and 11 at the same time

67: The difference between 20 times the last digit and the rest of the number is 0 or a multiple of 67

68: The number is a multiple of 4 and 17 at the same time

69: The number is a multiple of 3 and 23 at the same time

70: The number is a multiple of 7 and 10 at the same time

71: The difference between 7 times the last digit and the rest of the number is 0 or a multiple of 71

72: The number is a multiple of 8 and 9 at the same time

73: The sum of 22 times the last digit and the rest of the number is a multiple of 73

74: The number is a multiple of 2 and 37 at the same time

75: The number is a multiple of 3 and 25 at the same time

76: The number is a multiple of 4 and 19 at the same time

77: The number is a multiple of 7 and 11 at the same time

78: The number is a multiple of 2, 3 and 13 at the same time

79: The sum of 8 times the last digit and the rest of the number is a multiple of 79

80: The last 4 digits are a multiple of 80; the 1, 000s digit is even and the last 3 digits are 000 or a multiple of 80, or the 1, 000s digit is odd and the last 3 digits are the result of multiplying 40 by an odd number

81: The difference between 8 times the last digit and the rest of the number is 0 or a multiple of 81

82: The number is a multiple of 2 and 41 at the same time

83: The sum of 25 times the last digit and the rest of the number is a multiple of 83

84: The number is a multiple of 3, 4 and 7 at the same time

85: The number is a multiple of 5 and 17 at the same time

86: The number is a multiple of 2 and 43 at the same time

87: The number is a multiple of 3 and 29 at the same time

88: The number is a multiple of 8 and 11 at the same time

89: The sum of 9 times the last digit and the rest of the number is a multiple of 89

90: The number is a multiple of 9 and 10 at the same time

91: The number is a multiple of 7 and 13 at the same time

92: The number is a multiple of 4 and 23 at the same time

93: The number is a multiple of 3 and 31 at the same time

94: The number is a multiple of 2 and 47 at the same time

95: The number is a multiple of 5 and 19 at the same time

96: The number is a multiple of 3 and 32 at the same time

97: The difference between 29 times the last digit and the rest of the number is 0 or a multiple of 97

98: The number is a multiple of 2 and 49 at the same time

99: The number is a multiple of 9 and 11 at the same time

100: The number ends in 00

[marineroption]

from the bottom of my heart...THANK YOU..25 years ago when there were no you tube..if i dont undersatand a topic about math i have to walk 5 kilometers to my aunt who is a math teacher for her to explain it to me...now if my son having a problem about math i just click khan academy..from philippines thank you again

[kawaiipandajoy]

Your my
Thank You
Who needs human tutors
when ya got wifi right?
human tutors are expensive

[RSosage]

To check 8 you test if the last 3 digits are divisible by 8. Then it yields either yes or no

[Existencer]

check eight.
see last 3 digits
e.g. 54392 -> 392/8 = 49 same trick for checking 4.
4x25=100
8x125=1000
so check the last three digits

[gabixllabuilds]

Thank You! I needed to catch up at school, this helped me so much despite how old this is!❤️☺️

[avahsales]

Wow! i was having a really hard time understanding Divisibility but now i do thank you!

[ryanoliver]

You check seven as well! You take the last digit of a number and double it then subtract it from the number without the last digit. If the result is divisible by 7 or is 0, the original one was as well. You can keep repeating it to check it.

Example:

252 -> 25 - 2(2) = 21 -> 2 - 1(2) = 0. So 252 is divisible by 7. You could have stopped at 21 if you knew it was divisible by 7.

[Chaserooskii]

I do this in class it confuses me but this helpssss!!!

[NoActuallyGo-KCUF-Yourself]

Divide by 2 several times. If after the first division the quotient is a whole number, then div/2, divide by 2 again - quotient still a whole number? then div/4, divide by 2 again, quotient still a whole number? then div/8, etc.
For mental arithmetic it is often easier to find halves of even numbers than to divide by 8 straight out.
As a short cut, you can see if the quotient is odd, then you know that the next division will not yield a whole number.

[AlRoderick]

Very clever! But checking to see if a three-digit number is divisible by 8 isn't trivial. Admittedly, trying to find out if 872 is divisible by 8 is easier than 9, 326, 872, but it's not something you can do in your head easily. I suppose you can tell at a glance if it's not divisible by 4, and that would mean it's not divisible by 8, but is there a quick way to tell if a three-digit number known to be divisible by 4 is also divisible by eight?

[ilykiera]

3101
take off the last digit
310
double the digit removed (2) and subtract (-) to the remaining numbers
310 - 2 = 308
repeat process
30 - 16 = 14
14 is divisible by 7

as for 8
when dealing with a very large number, see if the last three digits are divisible by 8

[mariaagonzalez]

These videos help me study so much I’m so thankful that khan academy is a real thing without it, I will never be smart so thank you

[anafrancaisbolos]

Im in grade five rn and i am so glad there r still people like you to fill my head up!

[HAWXLEADER]

press quality settings choose 240p...
here is the old khan vids...
how did we manage to see something?
somehow it works perfectly!

sal please stop making hd remakes(even though it's neat)... it has no purpose....
just make new vids and make them hd.

btw you are the perfect teacher and a way of learning!(till the minds streaming comes lol)

[christiangab]

Thank you ! you are such a generous person ^^

[AlRoderick]

Just answered my own question. If the last 2 are divisible by 4 and the hundreds place is even, it's divisible by 8. So in this example, the first number isn't even though it's divisible by 4 since its hundreds place is odd.

[alijawed]

That you so much, it is helpful and also easy way to learn

[matiaspereira]

The divisibility rules of all numbers from 1 to 20

1: All numbers are multiples of 1

2: The number ends in 0, 2, 4, 6 or 8

3: The sum of its digits is a multiple of 3

4: The last 2 digits are a multiple of 4

5: The number ends in 0 or 5

6: The number is a multiple of 2 and 3 at the same time

7: The difference between twice the last digit and the other digits is a multiple of 7

8: The last 3 digits are a multiple of 8

9: The sum of its digits is a multiple of 9

10: The number ends in 0

11: The difference between the last digit and the other digits is a multiple of 11

12: The number is a multiple of 3 and 4 at the same time

13: The sum of 4 times the last digit and the other digits is a multiple of 13

14: The number is a multiple of 2 and 7 at the same time

15: The number is a multiple of 3 and 5 at the same time

16: The last 4 digits are a multiple of 16

17: The difference between 5 times the last digit and the other digits is a multiple of 17

18: The number is a multiple of 2 and 9 at the same time

19: The sum of twice the last digit and the other digits is a multiple of 19

20: The number ends in 00, 20, 40, 60 or 80

[twalker]

I'm sure he thought about whether it would be better for him to repeat himself or leave lots of pauses while he draws and writes. Perhaps you would prefer the gaps but Sal is a man who seems to know his audience