Calculations - Divisibility Rules - Practicing

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

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

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

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”

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

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

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

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

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

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