10. divisibility rules

Divisibility rules for 2, 3, 4, 5, 6, 8, and 9 with drills.

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, a nd 1 2 2 =6, no remainder. 528 is divisible by 4 , because 28 2= 14 , a nd 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 1 04 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 1 04 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 2 02 2 =1 01 , 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. 9 23 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!