Divisibility Rules Practice Quiz

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Janaisa Harris, BA-Mathematics |
Mathematics Expert
Review Board Member
Ms. Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher. She is now broadening her educational impact by engaging in curriculum mapping for her county. This endeavor enriches her understanding of educational strategies and their implementation. With a strong commitment to quality education, she actively participates in the review process of educational quizzes, ensuring accuracy and relevance to the curriculum.
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You must have read about the divisibility rules in your maths textbooks. Do you still remember those rules? If yes, play it out this practice quiz and test your knowledge for the same. A divisibility rule is a short and useful method to identify whether any given number is divisible by a fixed divisor without performing the actual division. The below quiz contains ten questions. Let's see how easily you solve it. Shall we begin it now? Good luck!

• 1.

If the sum of the digits of a number is divisible by 3, then the number will be divisible by which of the following?

• A.

3

• B.

9

• C.

2

• D.

7

A. 3
Explanation
If the sum of the digits of a number is divisible by 3, then the number will be divisible by 3 as well. This is because when a number is divisible by 3, the sum of its digits is also divisible by 3. Therefore, if the sum of the digits of a number is divisible by 3, it implies that the number itself is divisible by 3.

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• 2.

Which number is divisible by 2?

• A.

123

• B.

236

• C.

237

• D.

345

B. 236
Explanation
The number 236 is divisible by 2 because it ends in an even digit, which means it is an even number. In contrast, the other numbers listed (123, 237, and 345) do not end in even digits and are therefore not divisible by 2.

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• 3.

1000 can be divisible by which number here?

• A.

5

• B.

3

• C.

2

• D.

2 and 5 both

D. 2 and 5 both
Explanation
1000 can be divided evenly by both 2 and 5. When a number is divisible by 2, it means that it can be divided into two equal parts without leaving any remainder. Similarly, when a number is divisible by 5, it means that it can be divided into five equal parts without leaving any remainder. In the case of 1000, it can be divided by 2 to give 500 and by 5 to give 200. Therefore, the correct answer is that 1000 is divisible by both 2 and 5.

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• 4.

Which number is divisible by both 2 and 3?

• A.

126

• B.

100

• C.

123

• D.

133

A. 126
Explanation
The number 126 is divisible by both 2 and 3 because it is an even number (divisible by 2) and the sum of its digits (1+2+6) is 9, which is divisible by 3. Therefore, 126 satisfies the conditions of being divisible by both 2 and 3.

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• 5.

Which number is divisible by 9?

• A.

78500

• B.

78531

• C.

78532

• D.

78534

D. 78534
Explanation
The number 78534 is divisible by 9 because the sum of its digits is divisible by 9. In this case, 7+8+5+3+4=27, which is divisible by 9. Therefore, 78534 is divisible by 9.

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• 6.

Which number is divisible by both 3 and 9?

• A.

78531

• B.

78534

• C.

3333

• D.

1234

B. 78534
Explanation
The number 78534 is divisible by both 3 and 9 because the sum of its digits (7+8+5+3+4) is equal to 27, which is divisible by both 3 and 9.

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• 7.

15000 can be divisible by which number here?

• A.

2

• B.

3

• C.

5

• D.

All of the above

D. All of the above
Explanation
The number 15000 can be divided evenly by 2 because it is an even number. It can also be divided evenly by 3 because the sum of its digits (1+5+0+0+0) is divisible by 3. Additionally, it can be divided evenly by 5 because it ends in 0 or 5. Therefore, all of the given numbers (2, 3, and 5) can divide 15000 evenly.

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• 8.

What numbers are divisible by 2, 3, and 10 at the same time?

• A.

12

• B.

30

• C.

80

• D.

120

• E.

50

B. 30
D. 120
Explanation
The numbers that are divisible by 2, 3, and 10 at the same time are called common multiples. In this case, 30 and 120 are the common multiples. Both 30 and 120 can be divided evenly by 2, 3, and 10, making them the correct answers.

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• 9.

The number 203 is divisible by 3 and 7

• A.

True

• B.

False

B. False
Explanation
The number 203 is not divisible by 3 because the sum of its digits (2+0+3) is not divisible by 3. Additionally, 203 is not divisible by 7 because it does not end in a 7 or a 0. Therefore, the statement is false.

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• 10.

36 is divisible by

• A.

10

• B.

5

• C.

2

• D.

7

C. 2
Explanation
The number 36 is divisible by 2 because it is an even number.

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Janaisa Harris |BA-Mathematics |
Mathematics Expert
Ms. Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher. She is now broadening her educational impact by engaging in curriculum mapping for her county. This endeavor enriches her understanding of educational strategies and their implementation. With a strong commitment to quality education, she actively participates in the review process of educational quizzes, ensuring accuracy and relevance to the curriculum.

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• Current Version
• Mar 13, 2024
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Expert Reviewed by
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• Feb 23, 2022
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