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Calculations - Divisibility Rules - Practicing

How many of the number '8' are there in this quiz?

Calculations - Divisibility Rules - Practicing

This Math quiz is called 'Calculations - Divisibility Rules - Practicing' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.

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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!

If you have not taken the quiz DIVISIBILITY RULES - LEARNING then you might want to look at that quiz first before attempting this quiz as it will list each rule in detail with examples given for each rule. This quiz will continue your practice based off of those rules to see if you remember them and to see if you can work out the problems by following each rule.

So if you feel comfortable in being able to begin this quiz then move on to the following ten questions and see if you can find the right answer without looking back at the rules. (Remember, if you are not comfortable moving forward just yet, check out the DIVISIBILITY RULES - LEARNING quiz and then come back to this quiz and begin your practice.)

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
Author:  Christine G. Broome

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