What are the divisibility rules for 1 through 50?

Answer 1

1: Every 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
• 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 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 a multiple of 8
• The 100s digit is odd and the last 2 digits are 4 times 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 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 a multiple of 16
• The 1,000s digit is odd and the last 3 digits are 8 times an odd number

17: The difference between 5 times the last digit and the rest of the number 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 rest of the number is a multiple of 19

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

21: The difference between twice the last digit and the rest of the number is a multiple of 21

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 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 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 a multiple of 32
• The 10,000s digit is odd and the last 4 digits are 16 times an odd number

33: The sum of 10 times the last digit and the rest of the number is a multiple of 33

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 a multiple of 37

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

39: The sum of 4 times the last digit and the rest of the number is a multiple of 39

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
• 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 a multiple of 41

42: The number is a multiple of 2 and 21 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 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

Answer 2

Do the division, if there is no remainder, it is divisible. Seriously, many of the "divisibility rules" that have been discovered become more complicated than doing the actual division. For practical purposes, just learn the divisibility rules for a few simple cases (divisibility rules by 2, 4, 8, 5, 10, 3, 9, 7, 11, and 13), and for all other cases, just do the division.