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Number system questions

Aptitude Updated 11 Oct 2026

These number system questions cover HCF and LCM, divisibility rules, remainders, unit digits, prime numbers and factors, the building blocks of every aptitude test. Number system aptitude questions appear in SSC, bank, railway and campus placement papers, and they also make other topics like time and work or ratio easier.

The 31 questions are grouped into HCF and LCM, divisibility and remainders, and number properties. Each one shows the working in a few short steps so you can learn the shortcut.

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HCF and LCM aptitude questions

  1. Q1. Find the highest common factor of 36 and 84.

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    Answer: B. 12
    36 = 2 x 2 x 3 x 3 and 84 = 2 x 2 x 3 x 7. The common factors are 2 x 2 x 3 = 12.

  2. Q2. Find the lowest common multiple of 12, 15 and 20.

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    Answer: C. 60
    12 = 2^2 x 3, 15 = 3 x 5, 20 = 2^2 x 5. Take the highest powers: 2^2 x 3 x 5 = 60.

  3. Q3. The product of two numbers is 2160 and their HCF is 12. What is their LCM?

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    Answer: C. 180
    HCF x LCM = product of the two numbers, so LCM = 2160 / 12 = 180.

  4. Q4. What is the least two digit number which, when divided by 6, 8 and 12, leaves a remainder of 5 in each case?

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    Answer: B. 29
    LCM of 6, 8 and 12 is 24. Such numbers are of the form 24k + 5, giving 5, 29, 53 and so on. The least two digit one is 24 + 5 = 29.

  5. Q5. What is the greatest number that divides 43, 91 and 183 leaving the same remainder in each case?

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    Answer: D. 4
    Take the differences: 91 - 43 = 48, 183 - 91 = 92, 183 - 43 = 140. HCF of 48, 92 and 140 is 4.

  6. Q6. What is the HCF of the fractions 2/3, 4/9 and 8/15?

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    Answer: A. 2/45
    HCF of fractions = HCF of numerators / LCM of denominators = HCF(2, 4, 8) / LCM(3, 9, 15) = 2/45.

  7. Q7. Three bells ring at intervals of 6, 8 and 12 minutes. If they ring together at 9:00 a.m., when will they next ring together?

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    Answer: A. 9:24 a.m.
    The bells ring together after LCM(6, 8, 12) = 24 minutes, so the next time is 9:24 a.m.

  8. Q8. Two numbers are in the ratio 3 : 4 and their HCF is 5. What is their LCM?

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    Answer: D. 60
    The numbers are 3 x 5 = 15 and 4 x 5 = 20. LCM = 3 x 4 x 5 = 60.

  9. Q9. What is the greatest number that divides 1657 and 2037 leaving remainders 6 and 5 respectively?

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    Answer: C. 127
    Subtract the remainders: 1657 - 6 = 1651 and 2037 - 5 = 2032. HCF of 1651 and 2032 is 127.

  10. Q10. What is the largest four digit number exactly divisible by 12, 15 and 18?

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    Answer: A. 9900
    LCM of 12, 15 and 18 is 180. 9999 / 180 leaves remainder 99, so 9999 - 99 = 9900.

Divisibility, remainders and unit digit questions

  1. Q11. Using the digit sum rule, which of these numbers is divisible by 9?

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    Answer: C. 7452
    A number is divisible by 9 if its digit sum is divisible by 9. For 7452 the sum is 7 + 4 + 5 + 2 = 18.

  2. Q12. What is the smallest digit that can replace * in 4*16 so that the number is divisible by 3?

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    Answer: B. 1
    The known digits add to 4 + 1 + 6 = 11. The next multiple of 3 is 12, so * = 1 (4116 is divisible by 3).

  3. Q13. What is the remainder when 2^10 is divided by 7?

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    Answer: D. 2
    2^3 = 8 leaves remainder 1 when divided by 7. 2^10 = (2^3)^3 x 2, so the remainder is 1 x 2 = 2.

  4. Q14. A number leaves a remainder of 29 when divided by 56. What remainder will it leave when divided by 8?

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    Answer: A. 5
    56 is a multiple of 8, so only the remainder 29 matters. 29 divided by 8 leaves remainder 5.

  5. Q15. Using the alternate digit rule, which of these numbers is divisible by 11?

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    Answer: C. 95832
    For 95832 the difference between the sums of alternate digits is (9 + 8 + 2) - (5 + 3) = 11, which is divisible by 11.

  6. Q16. What is the remainder when 17^23 is divided by 16?

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    Answer: C. 1
    17 = 16 + 1, so 17 leaves remainder 1 when divided by 16. Any power of it also leaves 1^23 = 1.

  7. Q17. Including 1 and itself, how many factors does 72 have?

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    Answer: A. 12
    72 = 2^3 x 3^2. Number of factors = (3 + 1) x (2 + 1) = 12.

  8. Q18. When 7 is raised to the power 95, what digit appears in the units place?

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    Answer: B. 3
    Unit digits of powers of 7 repeat in the cycle 7, 9, 3, 1. 95 divided by 4 leaves remainder 3, so the unit digit is the third in the cycle, 3.

  9. Q19. What is the unit digit of 13^4 x 17^3?

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    Answer: D. 3
    13^4 ends in 1 (cycle 3, 9, 7, 1) and 17^3 ends in 3 (cycle 7, 9, 3, 1). 1 x 3 = 3, so the unit digit is 3.

  10. Q20. Find the sum 1 + 2 + 3 + ... + 20.

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    Answer: D. 210
    Use n(n + 1)/2: 20 x 21 / 2 = 210.

Prime numbers, factors and number properties

  1. Q21. Counting from 1 to 50, how many of the numbers are prime?

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    Answer: A. 15
    The primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47, which is 15 numbers.

  2. Q22. Only one of these four numbers is prime. Which one?

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    Answer: B. 97
    91 = 7 x 13, 87 = 3 x 29 and 51 = 3 x 17, but 97 has no factor other than 1 and itself.

  3. Q23. Find the sum 1 + 3 + 5 + ... + 19 of the first ten odd numbers.

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    Answer: A. 100
    The sum of the first n odd numbers is n^2, so 10^2 = 100.

  4. Q24. How many zeros are there at the end of 100 factorial, the product 1 x 2 x 3 x ... x 100?

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    Answer: D. 24
    Count the factors of 5: 100/5 = 20 and 100/25 = 4. Total = 20 + 4 = 24 trailing zeros.

  5. Q25. Using prime factors, find the square root of 1764.

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    Answer: C. 42
    1764 = 2^2 x 3^2 x 7^2, so its square root is 2 x 3 x 7 = 42.

  6. Q26. What is the least number that must be added to 1000 to make it exactly divisible by 23?

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    Answer: C. 12
    1000 divided by 23 gives quotient 43 and remainder 11. Add 23 - 11 = 12 to get 1012 = 23 x 44.

  7. Q27. What is the least number that must be subtracted from 2000 to make it a perfect square?

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    Answer: B. 64
    44^2 = 1936 and 45^2 = 2025. So subtract 2000 - 1936 = 64.

  8. Q28. What is the sum of all two digit numbers from 10 to 99?

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    Answer: A. 4905
    There are 90 numbers. Sum = number of terms x (first + last) / 2 = 90 x 109 / 2 = 4905.

  9. Q29. Which fraction is equal to the recurring decimal 0.454545...?

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    Answer: D. 5/11
    For a two digit repeating block, write it over 99: 45/99 = 5/11.

  10. Q30. What is the difference between the place value and the face value of 7 in 57,382?

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    Answer: B. 6993
    The place value of 7 in 57,382 is 7000 and its face value is 7. Difference = 7000 - 7 = 6993.

  11. Q31. The product of two coprime numbers is 117. What is their LCM?

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    Answer: B. 117
    Coprime numbers have HCF 1, and HCF x LCM = product. So LCM = 117 / 1 = 117.

How to prepare

For HCF and LCM questions, remember the key relation: HCF x LCM = product of the two numbers. When a question asks for the greatest number that divides several numbers with the same remainder, find the HCF of their differences. When it asks for the least number that leaves a fixed remainder, find the LCM and add that remainder.

For remainder and unit digit questions, look for a pattern instead of multiplying. Powers repeat their unit digits in cycles of 4, and a number just above a divisor (like 17 for 16) always leaves remainder 1 for any power. Learn the divisibility rules for 3, 9 and 11 by heart, because they save time in the first minute of many papers.

Study tips

  • Write every number as a product of prime factors first; HCF, LCM and number of factors all follow from it.
  • Memorise the unit digit cycles of 2, 3, 7 and 8 so you can answer power questions in seconds.
  • Check your HCF or LCM answer by testing that it divides, or is divided by, each given number.

More practice questions

Questions people ask

What is the shortcut for HCF and LCM aptitude questions?

Use prime factorisation: HCF takes the lowest power of common primes and LCM takes the highest power of all primes. For two numbers, HCF x LCM equals their product.

How do I find the unit digit of a large power?

Divide the power by 4 and use the remainder to pick the unit digit from the number's cycle. If the remainder is 0, use the fourth term of the cycle.

Which number system topics are most important for placement tests?

HCF and LCM, divisibility rules, remainders, unit digits and trailing zeros of factorials appear most often. All are covered on this page.

How do I find the number of factors of a number?

Write the number as a product of prime powers, add 1 to each power and multiply. For 72 = 2^3 x 3^2, the count is 4 x 3 = 12.

Every question on this page is written and fact-checked by the GK Quizzes team. Spotted a mistake? Tell us and we will fix it. How we make our questions.