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Quizzes > High School Quizzes > Mathematics

Divisibility Rules Practice Quiz

Practice challenging divisibility drills to ace math

Difficulty: Moderate
Grade: Grade 6
Study OutcomesCheat Sheet
Colorful paper art promoting Divisibility Rule Rally trivia quiz for high school students.

Easy
What condition must a whole number satisfy to be divisible by 2?
Its last digit is 0, 2, 4, 6, or 8
The sum of its digits is even
It ends with an odd number
It has more than one digit
A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, or 8). This rule applies regardless of the other digits in the number.
Which of these numbers is divisible by 5?
34
55
27
42
A number is divisible by 5 if it ends in 0 or 5. Among the options, only 55 ends with 5, hence it is divisible by 5.
Which rule correctly determines if a number is divisible by 3?
The last digit is 3
The sum of its digits is divisible by 3
It has an even last digit
Its digits are arranged in ascending order
A number is divisible by 3 if the sum of its digits is divisible by 3, which is a quick test to check this divisibility. This insight is key to determining divisibility without full division.
What is the correct rule to determine if a number is divisible by 10?
The number ends in 0
The number ends in 5
The number is even
The sum of its digits is 10
A number is divisible by 10 if its last digit is 0, which is the standard rule for divisibility by 10. This makes identifying multiples of 10 straightforward.
Which of the following numbers is divisible by both 2 and 3, and therefore by 6?
12
15
17
22
For a number to be divisible by 6, it must be divisible by both 2 and 3. Out of the options provided, 12 meets both criteria, being even and having digits that sum to 6.
Medium
Which of the following numbers is divisible by 4?
312
315
318
327
A number is divisible by 4 if the number formed by its last two digits is divisible by 4. Since the last two digits of 312 are 12 and 12 ÷ 4 = 3, 312 is divisible by 4.
Which of the following numbers is divisible by 8?
512
524
530
546
A number is divisible by 8 if its last three digits form a number that is divisible by 8. With 512, since 512 ÷ 8 = 64 exactly, it meets the criteria.
What is the divisibility rule for 9?
The last digit must be 9
The number is divisible by 3 and 6
The sum of its digits is divisible by 9
The difference between alternate digits is 0
The rule for divisibility by 9 is that if the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9. This method is quick and widely used in mental math.
Which of the following numbers is divisible by 4?
24
37
43
51
For divisibility by 4, the number formed by the last two digits must be divisible by 4. Here, 24 ÷ 4 equals 6, confirming that 24 is divisible by 4.
Which statement correctly describes divisibility by 6?
A number is divisible by 6 if it is divisible by both 2 and 3
A number is divisible by 6 if the sum of its digits is 6
A number is divisible by 6 if it ends in 6
A number is divisible by 6 if it has more than one even digit
Divisibility by 6 requires that the number satisfies both the divisibility rules for 2 and 3. This means the number must be even and the sum of its digits must be divisible by 3.
Which of the following correctly explains why 132 is divisible by both 3 and 4?
Because the sum of its digits is 6 (divisible by 3) and its last two digits form 32, which is divisible by 4
Because 132 is an even number and the product of its digits is 6
Because it ends with the digit 2 and its middle digit is 3
Because 1 and 3 are prime numbers
132 is divisible by 3 since 1+3+2 equals 6, which is divisible by 3, and it is divisible by 4 because the last two digits, 32, divided by 4 yield 8. Therefore, it meets both criteria.
When checking if a large number is divisible by 2, 3, and 5 simultaneously, which process is most efficient?
Check if its last digit is even, sum the digits to see if divisible by 3, and confirm it ends in 0 or 5
Divide the number by 2 and assume it is divisible by 3 without checking
Multiply the digits and test if the product equals 30
Verify that the number is prime and less than 10
The fastest method is to individually apply each divisibility rule: for 2, the last digit must be even; for 3, the sum of the digits must be divisible by 3; and for 5, the number must end in 0 or 5. This step-by-step method ensures accuracy.
Determine if the number 480 meets the criteria for divisibility by both 8 and 10.
480 is divisible by both because it ends with 0 and 480 ÷ 8 equals 60
480 is divisible by 10 but not by 8
480 is divisible by 8 but not by 10
480 does not meet the divisibility criteria for either
480 ends with a 0, satisfying the rule for divisibility by 10, and dividing 480 by 8 gives 60, which confirms divisibility by 8. Both conditions are met.
Which of the following is an effective method to test if 1,254 is divisible by 3?
Check if its last digit is 4
Add all its digits (1+2+5+4) and verify that the sum, 12, is divisible by 3
Multiply the digits together and check if the product equals 1,254
Compare the first and last digits
By adding the digits 1, 2, 5, and 4, we get 12, which is divisible by 3. This confirms that 1,254 is divisible by 3.
A number is known to be divisible by both 2 and 5. What must be true about its last digit?
It must be 0
It can be either 0 or 5
It must be 5
It must be an even number other than 0
Numbers divisible by 5 end in 0 or 5, but if they also must be divisible by 2, they must be even. The only even possibility is 0.
Hard
Which is the smallest three-digit number that is divisible by both 4 and 9?
108
112
116
120
Since a number divisible by both 4 and 9 must be divisible by their least common multiple (36), the smallest three-digit multiple of 36 is 108. This meets both divisibility criteria.
If a number is divisible by 2, 3, and 4, it must also be divisible by which of the following numbers?
6
12
18
24
A number divisible by 2, 3, and 4 is divisible by the least common multiple of these numbers, which is 12. This is a common method to combine multiple divisibility rules.
Which of the following numbers is divisible by 3, 4, and 5?
120
130
140
150
A number divisible by 3, 4, and 5 must be divisible by the least common multiple of these numbers (which is 60). Out of the options provided, 120 is the only number that fits this requirement.
If a number is divisible by 9, what additional condition must be met for it to be divisible by 18?
The number must be even
The sum of its digits must be even
It must end in an odd digit
It must contain at least one zero
Divisibility by 18 requires that a number is divisible by both 9 and 2. Since divisibility by 9 is already given, the number must also be even (divisible by 2) to be divisible by 18.
Which of the following pairs of digits cannot form the last two digits of a number that is divisible by 4?
12
38
64
80
For a number to be divisible by 4, the number formed by its last two digits must be divisible by 4. Among the choices, 38 divided by 4 does not yield an integer, so it cannot be the ending of a number divisible by 4.
0
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Study Outcomes

  1. Apply divisibility rules to determine if a number is divisible by common divisors such as 2, 3, 5, and 10.
  2. Analyze numerical patterns to quickly identify factors and multiples.
  3. Evaluate and select the correct divisibility rule for a variety of problems.
  4. Utilize divisibility rules to eliminate incorrect answer choices in time-sensitive scenarios.
  5. Create efficient problem-solving strategies for quick mental calculations during quizzes.

Divisibility Rules Worksheet Cheat Sheet

  1. Divisibility by 2 - A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). It's like spotting pairs at a dance - only evens get an invite! Divisibility Rules Worksheet
  2. Divisibility by 3 - Add up all the digits, and if that sum is divisible by 3, so is the number. Think of it as a team effort: the whole squad's strength matters, not just one player! Divisibility Rules Worksheet
  3. Divisibility by 4 - Check the last two digits: if that tiny number is divisible by 4, you're golden. It's like examining just the last scene of a movie to know the ending! Divisibility Rules Worksheet
  4. Divisibility by 5 - A number ends in 0 or 5, and it's instantly divisible by 5. Picture a high-five - only numbers ending with that friendly 5 or a perfect 0 get it! Divisibility Rules Worksheet
  5. Divisibility by 6 - Must be even (rule of 2) and its digits' sum divisible by 3. It's the ultimate teamwork test: pass both mini-challenges to win big! Divisibility Rules Worksheet
  6. Divisibility by 7 - Double the last digit and subtract it from the rest; if the result is divisible by 7, so is the original number. It's like a magic trick minus the hat - give it a try and amaze your friends! Divisibility Rules Worksheet
  7. Divisibility by 8 - Look at the last three digits: if that mini-number is divisible by 8, the whole number is too. Think of it as checking the VIP section only! Divisibility Rules Worksheet
  8. Divisibility by 9 - Sum all digits and if that total is a multiple of 9, you've got divisibility. It's like a secret handshake: only numbers in the 9-club qualify! Divisibility Rules Worksheet
  9. Divisibility by 10 - Ends in a zero, and you're in. Simple as a full stop at the end of a sentence - no extra drama! Divisibility Rules Worksheet
  10. Divisibility by 11 - Alternately subtract and add digits from left to right; if the result is a multiple of 11, you win. It's like a zig-zag path to success - give it a go! Divisibility Rules Worksheet
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