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Divisibility Rules Questions

Practice 64 Divisibility Rules questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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64
Total Questions
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14
Easy
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45
Medium
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5
Hard
Practice by Exam:Quantitative Aptitude(56)Mathematics(3)General Intelligence & Reasoning(1)Numerical Ability(1)Quantitative Aptitude@NUM: 63(1)Quantitative Aptitude@NUM: 72(1)Number System(1)

About Divisibility Rules — practice questions, PYQs & concepts

Divisibility Rules is a frequently-tested topic on Quantitative Aptitude, Mathematics, General Intelligence & Reasoning. ExamTest.live currently lists 64 Divisibility Rules questions spanning previous-year papers from 2026 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Divisibility Rules weight in competitive exams

Across our Divisibility Rules question bank, the largest sources are Quantitative Aptitude (56), Mathematics (3), General Intelligence & Reasoning (1), Numerical Ability (1) and Quantitative Aptitude@NUM: 63 (1). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 14 easy Divisibility Rules questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
  • Time yourself: Every question shows the average solve time so you can benchmark your speed against other students.
  • Read every explanation: Even on questions you got right — the explanation often surfaces a faster approach you can reuse.

All Divisibility Rules Questions(1–64 of 64)

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Q1hardmcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
6% accuracy
If the five-digit number is divisible by , and , then what is the value of ?
Q2hardmcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
3% accuracy
If is divisible by , then what is the value of ?
Q3mediummcqQuantitative AptitudeCompetitive Exam2026
7% accuracy
If the 6 digit number is completely divisible by 8, then the smallest integer in place of will be:
Q4mediummcqQuantitative AptitudeCompetitive Exam2026
21% accuracy
If is divisible by 9, the missing digit will be:
Q5mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If a 9-digit number 1039m837n is divisible by 72, then find the value of
n
2
−m
4


​
.
Q6mediummcqQuantitative AptitudeCompetitive Exam2026
25% accuracy
Find the number nearest to 51462, that is divisible by 8.
Q7easymcqQuantitative AptitudeSSC CGL2026
0% accuracy
The number 7918378 is divisible by:
Q8hardmcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
If the 6-digit number 608xy0 is divisible by both 3 and 11, then the non-zero digits in the hundred's place (x) and ten's place (y), respectively, are:
Q9mediummcqQuantitative AptitudeCompetitive Exam 20262026
33% accuracy
Which of the following numbers is divisible by 8?
Q10mediummcqQuantitative AptitudeCompetitive Exam 20262026
33% accuracy
If ∗ is a digit such that 7235∗ is divisible by 11, then the value of ∗ is:
Q11mediummcqQuantitative AptitudeCompetitive Exam Practice2026
33% accuracy
If is a two-digit number, then will be completely divisible by:
Q12easymcqQuantitative AptitudeSSC CGL2026
50% accuracy
Without actual division, find the remainder when 379843 is divided by 3.
Q13mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If the six-digit number 15x1y2 is divisible by 44, then the minimum value of (x+y) is equal to:
Q14mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
0% accuracy
Find the sum of the greatest and the smallest number which may replace k in the number 8130k36 so that the number is divisible by 8.
Q15mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If the 9-digit number 957x5y6z3 is divisible by 33, then what is the maximum value of (x+y+z)?
Q16easymcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
Which of the following numbers is perfectly divisible by ?
Q17easymcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If the seven digit number is divisible by , then the value of is:
Q18mediummcqNumber SystemCompetitive Exam2026
0% accuracy
Which of the following numbers is divisible by 72?
Q19easymcqQuantitative AptitudeCompetitive Exam2026
If the number 3727x4 is completely divisible by 8, then the smallest integer in place of x will be:
Q20mediummcqQuantitative AptitudeSSC CGL2026
If the 10-digit number 96530y15x8 is divisible by 72, then what is the value of (3x−7y) for the maximum value of x?
Q21mediummcqQuantitative AptitudeSSC CGL2026
If the seven-digit number 49x29y6 is divisible by 72, then what will be the value of (x+2y) for the largest value of x and y?
Q22mediummcqQuantitative AptitudeCompetitive Exam2026
Which of the following numbers is divisible by 11?
Q23mediummcqQuantitative AptitudeCompetitive Exam Practice2026
If a 9-digit number 389x6378y is divisible by 72, then the value of 6x+7y is:
Q24easymcqQuantitative AptitudeCompetitive Exam Practice2026
Which of the following numbers is divisible by 9?
Q25easymcqQuantitative AptitudeCompetitive Exam2026
Which of the following numbers is divisible by 11?
Q26mediummcqQuantitative AptitudeCompetitive Examination2026
The difference between the squares of two consecutive even integers is always divisible by:
Q27mediummcqQuantitative AptitudeSSC CGL2026
Which of the following is NOT divisible by 4?
Q28mediummcqMathematicsUP Police Constable2026
Which of the numbers given below is exactly divisible by 12?
Q29mediummcqQuantitative AptitudePractice Test2026
Find the least value of K for which 7864K3 is divisible by 7.
Q30mediummcqMathematicsUPTET 2021 Memory Based Paper 12026
The least positive digit , so that the number is divisible by 11 is:
Q31mediummcqQuantitative AptitudeStaff Selection Commission2026
If a nine-digit number 385x3678y is divisible by 72, then the value of (y−x) is:
Q32mediummcqQuantitative AptitudeSSC CGL2026
What should be the missing digit so that the number 275_476 becomes exactly divisible by 11?
Q33mediummcqQuantitative AptitudeSSC CGL2026
A number 35786X625 is completely divisible by 9. Find the smallest whole digit number in the place of 'X'.
Q34mediummcqQuantitative AptitudeSSC CGL2026
If the number 583_437 is completely divisible by 9, then the smallest whole number in the place of the blank digit will be:
Q35hardmcqQuantitative AptitudeUP Police Constable2026
Find the product of the sum of digits of the smallest -digit number divisible by and the sum of digits of the smallest -digit number divisible by .
Q36mediummcqQuantitative AptitudeCompetitive Exam2026
A -digit number is divisible by . Which digit can replace ?
Q37mediummcqMathematicsCompetitive Exams2026
If the number is completely divisible by , then the smallest whole number in place of will be:
Q38easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
Find the smallest number which should be added to to get a number divisible by .
Q39mediummcqQuantitative AptitudeCompetitive Exam2026
Find the value of such that a 6-digit number is divisible by 11.
Q40hardmcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
If the five-digit number 602xy is divisible by 7 and 33, then the value of (8x−3y) is:
Q41mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
Find the value of
3k
3
+4

​
such that the 6-digit number 310k0k is divisible by 6.
Q42easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
Find the value of k in the number 9314k8025 so that the number is divisible by 11.
Q43mediummcqNumerical AbilityUP Police Constable2026
Which of the numbers given below is exactly divisible by 24?
Q44mediummcqQuantitative AptitudeCompetitive Exam2026
Find the largest number which should replace P in the 7-digit number 87893P4 to make the number divisible by 4.
Q45mediummcqQuantitative AptitudeCompetitive Exam2026
Find the smallest non-zero value of k so that the 7-digit number 48397k5 is divisible by 9.
Q46mediummcqQuantitative AptitudeCompetitive Exam2026
Find the sum of all the possible values of k in the number 341k145k so that the number is divisible by 3.
Q47mediummcqQuantitative AptitudeCompetitive Exam2026
If the number 321a9246b is divisible by 72, then find the value of a
2
−b
2
.
Q48mediummcqQuantitative AptitudeCompetitive Exam2026
Find the largest value of k such that a 6-digit number 450k1k is divisible by 3.
Q49mediummcqQuantitative AptitudeCompetitive Exam2026
If the number 583a4a is divisible by 6, then what is the sum of all the possible values of a?
Q50mediummcqQuantitative Aptitude@NUM: 63Competitive Exam2026
Find the smallest 4-digit number divisible by 8, formed using the digits 0, 2, 3, 4, 6, 8 without any repetition.
Q51easymcqQuantitative Aptitude@NUM: 72Competitive Exam2026
Find the number nearest to which is divisible by .
Q52mediummcqQuantitative AptitudeCompetitive Exams2026
Which of the following numbers are divisible by 11?
(i) 29435417
(ii) 57463828
(iii) 57463824
(iv) 29435416
Q53mediummcqQuantitative AptitudeCompetitive Exam2026
Find the greatest 5-digit number divisible by 12.
Q54easymcqQuantitative AptitudeCompetitive Exam2026
Which of the following numbers is divisible by 4.
(i) 67920598
(ii) 618703592
(iii) 618703594
(iv) 67920590
Q55mediummcqQuantitative AptitudeCompetitive Exam2026
Ram gives a six-digit number 468312 to Shyam to check the divisibility. Shyam tells Ram that the number is divisible by 57. Shyam asks Ram, "If we rearrange the digits of this number in descending order, then by which number will it be always divisible?"
Q56mediummcqQuantitative AptitudeCompetitive Exam2026
The five-digit number 725yz is divisible by 15. What is the maximum possible value of the product of y and z?
Q57easymcqQuantitative AptitudeStaff Selection Commission2026
The number 1254216 is divisible by which of the following numbers?
Q58easymcqQuantitative AptitudeStaff Selection Commission2026
Which of the following numbers is divisible by 36 ?
Q59mediummcqQuantitative AptitudeSSC GD Constable2026
What is the least value of k, so that 23k57 is divisible by 3?
Q60mediummcqQuantitative AptitudeSSC Competitive Exams2026
If a number is divisible by both 11 and 13, then it must be:
Q61mediummcqQuantitative AptitudeSSC Competitive Exams2026
If a 9-digit number 937X728Y6 is divisible by 72, then one of the possible values of X+Y is:
Q62easymcqQuantitative AptitudeSSC CGL2026
Which of the following numbers is divisible by 11?
Q63mediummcqGeneral Intelligence & ReasoningStaff Selection Commission2026
Four options have been given out of which three are alike in some manner, while one is different. Choose the odd one.
Q64mediummcqQuantitative AptitudeCompetitive Exams2026
A 4-digit number '34PQ' is divisible by 3, 5 and 7. Find the value of P+Q.

Frequently Asked Questions

How many Divisibility Rules questions are on ExamTest.live?▼
We have 64 Divisibility Rules questions spread across 1 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
Are Divisibility Rules MCQs free?▼
Yes. All Divisibility Rules questions, answers, and explanations on ExamTest.live are completely free. No account or subscription required.
Which exams include Divisibility Rules questions?▼
Divisibility Rules questions are commonly asked in Quantitative Aptitude, Mathematics, General Intelligence & Reasoning, Numerical Ability, Quantitative Aptitude@NUM: 63. You can filter by exam using the links above.
How do I practice Divisibility Rules questions effectively?▼
Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.