Practice Questions
Concept Explanation
A factor divides a number exactly. A multiple is obtained by multiplying the number by a positive integer.
Example: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Multiples of 6 are 6, 12, 18, 24, …
Key Facts
- Every number has at least two factors: 1 and itself.
- 1 is neither prime nor composite.
- If a divides b and b divides c, then a divides c.
- Common multiples help in LCM problems; common factors help in HCF problems.
Placement Tips
List factors systematically in pairs (1×n, 2×…). For large numbers, use prime factorisation to count factors quickly.
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Q1 Easy
How many factors does 36 have?
Explanation36 = 2² × 3². Number of factors = (2+1)(2+1) = 9. -
Q2 Easy
Which is a factor of 84?
Explanation84 ÷ 21 = 4 exactly, so 21 is a factor. The others leave a remainder. -
Q3 Easy
What is the 8th multiple of 7?
ExplanationThe 8th multiple of 7 is 7 × 8 = 56. -
Q4 Medium
How many multiples of 4 lie strictly between 11 and 49?
ExplanationMultiples: 12, 16, 20, 24, 28, 32, 36, 40, 44, 48. Count = (48−12)/4 + 1 = 10. -
Q5 Medium
Which number has exactly 3 factors?
ExplanationOnly squares of primes have exactly 3 factors: 1, p, p². 9 = 3² has factors 1, 3, 9. -
Q6 Medium
The sum of all factors of 12 is:
ExplanationFactors of 12: 1, 2, 3, 4, 6, 12. Sum = 28. -
Q7 Easy
If 15 is a factor of N, which must also divide N?
Explanation15 = 3 × 5, so any multiple of 15 is divisible by 3 and 5. Among options, 3 must divide N.
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Q8 Medium
How many numbers less than 100 are multiples of both 3 and 5?
ExplanationMultiples of lcm(3,5)=15 below 100: 15,30,45,60,75,90 → 6 numbers. -
Q9 Easy
Which pair are both factors of 72?
Explanation72 ÷ 12 = 6 and 72 ÷ 18 = 4. Both divide exactly. -
Q10 Easy
The largest factor of 56 other than 56 itself is:
ExplanationFactors of 56 include 28; 28 × 2 = 56. So 28 is the largest proper factor. -
Q11 Hard
How many even factors does 60 have?
Explanation60 = 2² × 3 × 5. Total factors = 12. Odd factors from 3×5 = 4. Even factors = 12 − 4 = 8. -
Q12 Easy
If x is a multiple of 6 and 6 < x < 20, how many values can x take?
ExplanationMultiples: 12, 18. Two values. -
Q13 Medium
Which is NOT a multiple of 11?
Explanation145 ÷ 11 = 13 remainder 2, so 145 is not a multiple of 11. The others are multiples of 11. -
Q14 Medium
The number of factors of 48 is:
Explanation48 = 2⁴ × 3. Number of factors = (4+1)(1+1) = 10.
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DS1 Medium
Is N divisible by 12?
Statement IN is a multiple of 6.
Statement IIN is a multiple of 4.
ExplanationN multiple of 6 does not guarantee divisibility by 4 (e.g. 6). N multiple of 4 does not guarantee divisibility by 3 (e.g. 4). Both together: lcm(6,4)=12, so N is a multiple of 12. -
DS2 Easy
How many factors does N have?
Statement IN = 2³ × 5.
Statement IIN is a perfect square.
ExplanationFrom prime form, number of factors = (3+1)(1+1) = 8. Statement II alone does not identify N.
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DS3 Hard
Is N greater than 50?
Statement IN has 6 factors.
Statement IIN is a multiple of 13.
ExplanationSix factors could be 12, 18, 20, 28, 32, 44, etc. Multiples of 13 include 13, 26, 39, 52… Neither alone nor together fixes whether N > 50. -
DS4 Medium
What is the sum of factors of N?
Statement IN = 36.
Statement IIN is divisible by 9.
ExplanationN = 36 alone gives sum of factors = 91. Statement II with N=9 gives sum 13 but N is not fixed to 36.