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In an earlier quiz you learned that figuring out many division problems can be made easier when you know the basic divisibility rules. It took until you got to the 8th grade for anyone to spill the beans on that secret. With the divisibility rules - division, in many ways, seems a lot easier and even fun!

1.

Which of the following numbers are evenly divisible by the number “1”?

79538

52375

36821

Each one is evenly divisible by the number “1”

Per Rule 1, all numbers are evenly divisible by the number “1”. This means that Answer (d) is correct

2.

Which of the following numbers are evenly divisible by the number “2”?

16594

27653

45971

Each one is evenly divisible by the number “2”

Rule 2 tells us that if a number ends with a 0, 2, 4, 6 or 8 then that number, no matter how long it is, will be evenly divisible by the number “2”. Neither Answer (b) nor Answer (c) ends in one of these numbers so they are not evenly divisible by the number “2”. Answer (a) does end with the number “4” and 16594 ÷ 2 = 8297. Answer (a) is the correct answer

3.

Which of the following numbers are evenly divisible by the number “3”?

22526

58671

70921

Each one is evenly divisible by the number “3”

Rule 3 tells us that if the combined sum of the number is divisible by the number 3, then the entire number is evenly divisible by the number “3”. Answer (a) would then be 2 + 2 + 5 + 2 + 6 = 17. The number 17 is not evenly divisible by the number “3” so it is not the correct answer. Answer (c) would be 7 + 0 + 9 + 2 + 1 = 19. The number 19 is not evenly divisible by the number “3” so Answer (c) is not the correct answer. Answer (b) would be 5 + 8 + 6 + 7 + 1 = 27. The number 27 is evenly divisible by the number “3” in that 27 ÷ 3 = 9. Answer (b) is the correct answer

4.

Which of the following numbers are evenly divisible by the number “4”?

69016

39836

74520

Each one is evenly divisible by the number “4”

Rule 4 tells us that if the last two digits of a number are divisible by the number “4” then the entire number is evenly divisible by the number “4”. The last two digits of Answer (a) are 16. The number 16 is evenly divisible by the number “4” in that 16 ÷ 4 = 4 so the entire number should also be evenly divisible by the number “4” so 69016 ÷ 4 = 17254 so this answer is correct. The last two digits of Answer (b) are 36. The number 36 is evenly divisible by the number “4” in that 36 ÷ 4 = 9 and then 39836 ÷ 4 = 9959 so it is also correct. The last two digits of Answer (c) are 20. The number 20 is evenly divisible by the number “4” in that 20 ÷ 4 = 5 and then 74520 ÷ 4 = 18630 making it also correct. Therefore, Answer (d) is the correct answer as each number is evenly divisible by the number “4”

5.

Which of the following numbers are evenly divisible by the number “5”?

12800

14982

15156

Each one is evenly divisible by the number “5”

Rule 5 tells us that if the last digit of a number is either a 0 or a 5, then the entire number is evenly divisible by the number “5”. The last digit on Answers (b) and (c) is not a “0” nor a “5” so neither of them is the correct answer. The last digit on Answer (a) is a “0” so the entire number should be evenly divisible by the number “5”. Let’s check that. 12800 ÷ 5 = 2560. Answer (a) is the correct answer

6.

Which of the following numbers are evenly divisible by the number “6”?

48743

90824

61956

Each one is evenly divisible by the number “6”

Rule 6 tells us that if the last digit of a number is divisible by the number “2” and the sum of all the numbers is divisible by the number “3” then the entire number can be evenly divisible by the number “6”. The last digit of Answer (a) is not evenly divisible by the number “2” so this answer is not correct. The last digit of Answer (b) is evenly divisible by the number “2” in that 4 ÷ 2 = 2. Now let’s see if the sum of the numbers will be evenly divisible by the number “3”. 9 + 0 + 8 + 2 + 4 = 23. The number “23” is not evenly divisible by the number “3” so this answer is also not correct. The last digit of Answer (c) is evenly divisible by the number “2” in that 6 ÷ 2 = 3. Now let’s see what the sum of the numbers are. 6 + 1 + 9 + 5 + 6 = 27. The number 27 ÷ 3 = 9. Now the entire number should be evenly divisible by the number “6” so let’s check that out. 61956 ÷ 6 = 10326. Answer (c) is the correct answer

7.

Which of the following numbers are evenly divisible by the number “9”?

50086

89874

34879

Each one is evenly divisible by the number “9”

Rule 7 tells us that if the sum of all of the digits is evenly divisible by the number “9” then the entire number is evenly divisible by the number “9”. Answer (a) is 5 + 0 + 0 + 8 + 6 = 19. The number 19 is not evenly divisible by the number “9” so this is not the correct answer. Answer (c) is 3 + 4 + 8 + 7 + 9 = 31. The number 31 is not evenly divisible by the number “9” so this is not the correct answer. Answer (b) is 8 + 9 + 8 + 7 + 4 = 36. The number 36 is evenly divisible by the number “9” in that 36 ÷ 9 = 4. This means the entire number should be evenly divisible by the number “9” so 89874 ÷ 9 = 9986. Answer (b) is the correct answer

8.

Which of the following numbers are evenly divisible by the number “10”?

198640

258510

625930

Each one is evenly divisible by the number “10”

Rule 8 tells us that if the last digit of a number is “0” then the entire number is evenly divisible by the number “10”. Answers (a), (b) and (c) all end in a “0” so let’s see if they are each evenly divisible by the number “10”. Answer (a) is 198640 ÷ 10 = 19864. Answer (b) is 258510 ÷ 10 = 25851. Answer (c) is 625930 ÷ 10 = 62593. Each answer is evenly divisible by the number “10” so Answer (d) is the correct answer

9.

Which of the following numbers are evenly divisible by the number “11”?

418653

639284

927421

Each one is evenly divisible by the number “11”

Rule 9 tells us that if you have a number and, moving left to right, you subtract every second number from its preceding number and then you add the remaining numbers, if their sum is divisible by the number “11”, then the entire number is evenly divisible by the number “11”. Starting with Answer (a) you have 4 - 1 = 3 and then 8 - 6 = 2 and then 5 - 3 = 2 which then gives you 3 + 2 + 2 = 7, the number “7” is not evenly divisible by the number “11” so it is not the correct answer. Answer (b) gives us 6 - 3 = 3 and 9 - 2 = 7 and 8 - 4 = 4 which then gives you 3 + 7 + 4 = 14, the number “14” is not evenly divisible by the number “11” so it is not the correct answer. Finally, Answer (c) gives us 9 - 2 = 7 and 7 - 4 = 3 and 2 - 1 = 1 which then gives us 7 + 3 + 1 = 11 and the number “11” is evenly divisible by the number “11” in that 11 ÷ 11 =1 making Answer (c) the correct answer

10.

Which of the following numbers are evenly divisible by the number “12”?

39628

54936

76924

Each one is evenly divisible by the number “12”

Rule 10 tells us that if the number is evenly divisible by both the numbers “3” and “4” then the entire number will be evenly divisible by the number “12”. In Answer (a) the sum of the number is 3 + 9 + 6 + 2 + 8 = 28. The number 28 is not evenly divisible by the number “3” so this is not the correct answer. In Answer (c) the sum of the number is 7 + 6 + 9 + 2 + 4 = 28. The number 28 is not evenly divisible by the number “3” so this is not the correct answer. In Answer (b) the sum of the number is 5 + 4 + 9 + 3 + 6 = 27. The number 27 is evenly divisible by the number “3” in that 27 ÷ 3 = 9. The last two digits are 36 and 36 is evenly divisible by the number “4” in that 36 ÷ 4 = 9. Now the entire number should be evenly divisible by the number “12” so 54936 ÷ 12 = 4578. Answer (b) is the correct answer

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