This document provides rules for determining if a number is divisible by other numbers without doing calculations. It explains: - A number is divisible by another if the result of dividing them is a whole number - Zero is divisible by any number - To check if a number is divisible by 2, look if it ends in 0, 2, 4, 6, or 8 - To check if a number is divisible by 3, add the digits and see if the sum is divisible by 3 - To check if a number is divisible by 6, see if it is divisible by both 2 and 3 - Other rules include checking the last digits or doing multiple divisions to determine divisibility by 4, 5, 8, or

1. By John Rome R. Aranas
DIVISIBILITY RULES

2. Divisibility Rules
Definition of Terms
These rules let you test if one
number is divisible by another,
without having to do too much
calculation!

3. “Divisible by”
Definition of Terms
It means "when you divide one
number by another the result is a
whole number"
EXAMPLES:
12 is divisible by 6, because 12 ÷ 6 = 2
15 is divisible by 3, because 15 ÷ 3 = 3
16 is not divisible by 5, because 16 ÷ 5 = 3r2

4. TRIVIA
Definition of Terms
Zero (0) is divisible to ANY
NUMBER

5. Divisible by 2
If the number ends in 0, 2, 4, 6,
or 8
EXAMPLES:
14 is divisible by 2, because it ends in 4
452 is divisible by 2, because it ends in 2
273 is not divisible by 2, because it does
not end in 0, 2, 4, 6, or 8

6. Divisible by 2
Say “YES” if the number is
DIVISIBLE BY 2. “NO” IF NOT.
54 YES!

7. Divisible by 2
Say “YES” if the number is
DIVISIBLE BY 2. “NO” IF NOT.
283 NO!

8. Divisible by 2
Say “YES” if the number is
DIVISIBLE BY 2. “NO” IF NOT.
872
YES!

9. Divisible by 2
Say “YES” if the number is
DIVISIBLE BY 2. “NO” IF NOT.
987 NO!

10. Divisible by 2
Say “YES” if the number is
DIVISIBLE BY 2. “NO” IF NOT.
5,267
NO!

11. Divisible by 3
If the sum of the digits is
divisible by 3.
EXAMPLES:
15 is divisible by 3, because 1+5=6, 6÷3=2
453 is divisible by 3, because
4+5+3=12, 12÷3=4
947 is not divisible by 3, because
9+4+7=20, 20÷3=6r2

12. Divisible by 3
Say “YES” if the number is
DIVISIBLE BY 3. “NO” IF NOT.
54 YES!

13. Divisible by 3
Say “YES” if the number is
DIVISIBLE BY 3. “NO” IF NOT.
837 YES!

14. Divisible by 3
Say “YES” if the number is
DIVISIBLE BY 3. “NO” IF NOT.
123
YES!

15. Divisible by 3
Say “YES” if the number is
DIVISIBLE BY 3. “NO” IF NOT.
687 NO!

16. Divisible by 3
Say “YES” if the number is
DIVISIBLE BY 3. “NO” IF NOT.
3,267
YES!

17. Divisible by 4
If the last 2 digits are divisible by 4
or both zeroes (00).
EXAMPLES:
24 is divisible by 4, because 24÷4=6
673 is not divisible by 4, because 73÷4=18r1
528 is divisible by 4, because 28÷4=7

18. Divisible by 4 (Alternate Rule)
Divide the last 2 digits by 2, 2 times.
If there’s no remainder, then the
number is divisible by 4.
EXAMPLES:
24 is divisible by 4, because 24÷2=12,
and 12÷2=6, no remainder.
528 is divisible by 4, because 28÷2=14,
and 14÷2=7, no remainder.

19. Divisible by 4
Say “YES” if the number is
DIVISIBLE BY 4. “NO” IF NOT.
32
YES!

20. Divisible by 4
Say “YES” if the number is
DIVISIBLE BY 4. “NO” IF NOT.
615 NO!

21. Divisible by 4
Say “YES” if the number is
DIVISIBLE BY 4. “NO” IF NOT.
761 NO!

22. Divisible by 4
Say “YES” if the number is
DIVISIBLE BY 4. “NO” IF NOT.
900 YES!

23. Divisible by 4
Say “YES” if the number is
DIVISIBLE BY 4. “NO” IF NOT.
3,000
YES!

24. Divisible by 5
If the number ends in 0 or 5.
EXAMPLES:
99 is not divisible by 5, because
it doesn’t end in 0 or 5.
875 is divisible by 5, because it ends in 5
1,280 is divisible by 5, because it ends in 0

25. Divisible by 5
Say “YES” if the number is
DIVISIBLE BY 5. “NO” IF NOT.
63 NO!

26. Divisible by 5
Say “YES” if the number is
DIVISIBLE BY 5. “NO” IF NOT.
890
YES!

27. Divisible by 5
Say “YES” if the number is
DIVISIBLE BY 5. “NO” IF NOT.
761 NO!

28. Divisible by 5
Say “YES” if the number is
DIVISIBLE BY 5. “NO” IF NOT.
805 YES!

29. Divisible by 5
Say “YES” if the number is
DIVISIBLE BY 5. “NO” IF NOT.
8,765
YES!

30. Divisible by 6
If the number is divisible by BOTH 2 and 3.
EXAMPLES:
67 is not divisible by 6, because
it not divisible by both 2 and 3.
682 is not divisible by 6, because
it is not divisible by 3.
978 is divisible by 6, because
it is divisible by both 2 and 3.

31. Divisible by 6
Say “YES” if the number is
DIVISIBLE BY 6. “NO” IF NOT.
54 YES!

32. Divisible by 6
Say “YES” if the number is
DIVISIBLE BY 6. “NO” IF NOT.
543 NO!

33. Divisible by 6
Say “YES” if the number is
DIVISIBLE BY 6. “NO” IF NOT.
782
YES!

34. Divisible by 6
Say “YES” if the number is
DIVISIBLE BY 6. “NO” IF NOT.
657 NO!

35. Divisible by 6
Say “YES” if the number is
DIVISIBLE BY 6. “NO” IF NOT.
1,628
NO!

36. Divisible by 8
If the last 3 digits are divisible by 8
or all zeroes (000).
EXAMPLES:
104 is divisible by 8, because 104÷8=13
1,000 is divisible by 8, because
it ends in 3 zeroes
7,808 is divisible by 8, because 808÷8=101

37. Divisible by 8 (Alternate Rule)
Divide the last 3 digits by 2, 3 times.
If there’s no remainder, then the
number is divisible by 8.
EXAMPLES:
104 is divisible by 8, because 104÷2=52,
52÷2=26, and 26÷2=13, no remainder.
7,808 is divisible by 8, because 808÷2=404,
404÷2=202, and 202÷2=101, no remainder.

38. Divisible by 8
Say “YES” if the number is
DIVISIBLE BY 8. “NO” IF NOT.
62 NO!

39. Divisible by 8
Say “YES” if the number is
DIVISIBLE BY 8. “NO” IF NOT.
800
YES!

40. Divisible by 8
Say “YES” if the number is
DIVISIBLE BY 8. “NO” IF NOT.
923 NO!

41. Divisible by 8
Say “YES” if the number is
DIVISIBLE BY 8. “NO” IF NOT.
7,000
YES!

42. Divisible by 8
Say “YES” if the number is
DIVISIBLE BY 8. “NO” IF NOT.
8,768
YES!

43. Divisible by 9
If the sum of the digits is
divisible by 9.
EXAMPLES:
18 is divisible by 9, because 1+8=9, 9÷9=1
387 is divisible by 9, because
3+8+7=18, 18÷9=2
789 is not divisible by 9, because
7+8+9=24, 24÷9=2r6

44. Divisible by 9
Say “YES” if the number is
DIVISIBLE BY 9. “NO” IF NOT.
54 YES!

45. Divisible by 9
Say “YES” if the number is
DIVISIBLE BY 9. “NO” IF NOT.
837 YES!

46. Divisible by 9
Say “YES” if the number is
DIVISIBLE BY 9. “NO” IF NOT.
567
YES!

47. Divisible by 9
Say “YES” if the number is
DIVISIBLE BY 9. “NO” IF NOT.
784 NO!

48. Divisible by 9
Say “YES” if the number is
DIVISIBLE BY 9. “NO” IF NOT.
7,623
YES!