ULTRA-TRICKY MCQs – GRADE 6 MATHS (DIVISIBILITY OF WHOLE NUMBERS








PRIME, COMPOSITE & CO-PRIME


1. Which is the smallest composite number ?
Options: (a) 1 (b) 2 (c) 3 (d) 4
Ans: (d) 4
Explanation: Composite numbers have more than two factors.

2. How many prime numbers are there between 1 and 10?
Options: (a) 3 (b) 4 (c) 5 (d) 6
Ans: (b) 4
Explanation: 2, 3, 5, 7.

3. Which number is neither prime nor composite?
Options: (a) 0 (b) 1 (c) 2 (d) 3
Ans: (b) 1
Explanation: 1 has only one factor.

4. The only even prime number is:
Options: (a) 1 (b) 2 (c) 4 (d) 6
Ans: (b) 2
Explanation: Every other even number is divisible by 2.

5. Which pair is co-prime?
Options: (a) 8 & 12 (b) 9 & 28 (c) 15 & 20 (d) 21 & 27
Ans: (b) 9 & 28
Explanation: Only common factor is 1.

6. If two numbers are co-prime, their HCF is:
Options: (a) 0 (b) 1 (c) 2 (d) Their product
Ans: (b) 1

7. Which is the smallest prime number greater than 50?
Options: (a) 51 (b) 53 (c) 55 (d) 57
Ans: (b) 53

8. The number with exactly three factors is:
Options: (a) 4 (b) 6 (c) 8 (d) 10
Ans: (a) 4
Explanation: Factors → 1,2,4.

9. Which is NOT a prime number ?
Options: (a) 31 (b) 37 (c) 39 (d) 41
Ans: (c) 39
Explanation: 39 = 3 × 13.

10. The sum of two prime numbers is always:
Options: (a) Even (b) Odd (c) Prime (d) Composite
Ans: (a) Even
Explanation: Except 2, primes are odd → odd+odd=even.

Divisibility Rules


11. A number is divisible by 3 if:
Options: (a) Last digit even (b) Sum of digits divisible by 3 (c) Ends in 5 (d) Last two digits divisible by 4
Ans: (b)

12. Which is divisible by 9 ?
Options: (a) 234 (b) 235 (c) 236 (d) 237
Ans: (a)
Explanation: 2+3+4=9.

13. A number is divisible by 4 if:
Options: (a) Last digit divisible by 4
(b) Last two digits divisible by 4
(c) Digit sum divisible by 4
(d) Ends in 4
Ans: (b)

14. Which is divisible by 6 ?
Options: (a) 124 (b) 126 (c) 127 (d) 129
Ans: (b)
Explanation: Divisible by 2 and 3.

15. Which number is divisible by 11 ?
Options: (a) 121 (b) 123 (c) 125 (d) 127
Ans: (a)

HCF & LCM


16. HCF of 12 and 18 is:
Options: (a) 3 (b) 6 (c) 9 (d) 12
Ans: (b)

17. LCM of 4 and 5 is:
Options: (a) 10 (b) 15 (c) 20 (d) 25
Ans: (c)

18. If HCF = 1, numbers are:
Options: (a) Composite (b) Co-prime (c) Even (d) Odd
Ans: (b)

19. Product of two numbers = HCF × ?
Options: (a) Sum (b) Difference (c) LCM (d) Quotient
Ans: (c)

20. LCM of 6 and 8 is:
Options: (a) 12 (b) 24 (c) 36 (d) 48
Ans: (b)


Remainder / Logic


21. Remainder when 100 is divided by 9:
Options: (a) 0 (b) 1 (c) 2 (d) 4
Ans: (b)

22. Smallest number to add to 199 to make it divisible by 5:
Options: (a) 1 (b) 2 (c) 3 (d) 4
Ans: (a)

23. Smallest number divisible by 2,3,5:
Options: (a) 10 (b) 20 (c) 30 (d) 60
Ans: (c)

24. Greatest 2-digit number divisible by 7:
Options: (a) 91 (b) 94 (c) 96 (d) 98
Ans: (d)

25. Least number leaving remainder 1 when divided by 2,3,4:
Options: (a) 11 (b) 13 (c) 15 (d) 17
Ans: (b)

PATTERN / TRICKY


26. Which has the most factors?
Options: (a) 16 (b) 17 (c) 19 (d) 23
Ans: (a)

27. Prime factorization of 36:
Options: (a) 2²×3² (b) 6×6 (c) 4×9 (d) 12×3
Ans: (a)

28. Odd × Odd = ?
Options: (a) Even (b) Odd (c) Prime (d) Zero
Ans: (b)

29. Even × Odd = ?
Options: (a) Even (b) Odd (c) Prime (d) Composite
Ans: (a)

30. Which is a multiple of both 8 and 9?
Options: (a) 36 (b) 48 (c) 72 (d) 96
Ans: (c)

ULTRA-TRICKY MCQs – GRADE 6 MATHS (DIVISIBILITY)













 













31. Greatest number dividing 45 and 75 exactly:
Options: (a) 5 (b) 10 (c) 15 (d) 25
Ans: (c) 15
Explanation: HCF of 45 and 75 is 15.

32. LCM of 9 and 12 is:
Options: (a) 18 (b) 24 (c) 36 (d) 48
Ans: (c) 36

33. How many multiples of 5 are between 1 and 50?
Options: (a) 5 (b) 8 (c) 10 (d) 12
Ans: (c) 10
Explanation: 5×10=50.

34. Smallest number divisible by 7 and 8:
Options: (a) 54 (b) 56 (c) 64 (d) 72
Ans: (b) 56

35. Which number leaves remainder 0 when divided by 3?
Options: (a) 221 (b) 222 (c) 223 (d) 224
Ans: (b) 222
Explanation: Digit sum = 6.

36. The HCF of two consecutive numbers is always:
Options: (a) 0 (b) 1 (c) 2 (d) Same number
Ans: (b) 1

37. Which is the smallest multiple of 13 greater than 100?
Options: (a) 104 (b) 117 (c) 130 (d) 143
Ans: (a) 104

38. Which number is divisible by 2, 4, and 8?
Options: (a) 16 (b) 18 (c) 24 (d) 32
Ans: (d) 32
Explanation: Must be a multiple of 8.

39. Greatest 3-digit multiple of 4:
Options: (a) 996 (b) 994 (c) 992 (d) 998
Ans: (a) 996

40. LCM of two co-prime numbers 8 and 15:
Options: (a) 60 (b) 120 (c) 30 (d) 45
Ans: (b) 120

41. Smallest number added to 888 to make it divisible by 5:
Options: (a) 1 (b) 2 (c) 3 (d) 4
Ans: (b) 2

42. Which is NOT divisible by 9?
Options: (a) 729 (b) 648 (c) 705 (d) 702
Ans: (c) 705

43. If LCM = HCF, the numbers are:
Options: (a) Co-prime
(b) Equal
(c) Prime
(d) Odd
Ans: (b) Equal

44. Smallest prime factor of 91:
Options: (a) 3 (b) 5 (c) 7 (d) 11
Ans: (c) 7

45. Which has exactly two factors?
Options: (a) Prime number
(b) Composite number
(c) Even number
(d) Multiple
Ans: (a)

46. Number divisible by 10 must end with:
Options: (a) 5 (b) 0 (c) Even digit (d) 2
Ans: (b)

47. Which number is divisible by both 6 and 9?
Options: (a) 18 (b) 27 (c) 36 (d) 45
Ans: (c) 36

48. HCF of 16 and 24:
Options: (a) 4 (b) 6 (c) 8 (d) 12
Ans: (c) 8

49. Greatest number that divides 100 and 125:
Options: (a) 5 (b) 10 (c) 20 (d) 25
Ans: (d) 25

50. Smallest multiple of 11 greater than 200:
Options: (a) 209 (b) 210 (c) 211 (d) 220
Ans: (a) 209

51. Which number is divisible by 4 but NOT by 8?
Options: (a) 16 (b) 24 (c) 32 (d) 40
Ans: (b) 24

52. The sum of digits of a number is 18. It is definitely divisible by:
Options: (a) 2 (b) 3 (c) 4 (d) 5
Ans: (b)

53. Least number divisible by 3, 4, and 6:
Options: (a) 6 (b) 12 (c) 18 (d) 24
Ans: (b) 12

54. Which number is a factor of every number?
Options: (a) 0 (b) 1 (c) 2 (d) 10
Ans: (b)

55. Which is the greatest prime number less than 30?
Options: (a) 23 (b) 25 (c) 29 (d) 27
Ans: (c)

56. If a number is divisible by 5 and 2, it must be divisible by:
Options: (a) 7 (b) 10 (c) 12 (d) 15
Ans: (b)

57. How many factors does a prime number have?
Options: (a) 1 (b) 2 (c) 3 (d) Many
Ans: (b)

58. Which is a multiple of both 12 and 15?
Options: (a) 30 (b) 45 (c) 60 (d) 75
Ans: (c)

59. Greatest multiple of 9 less than 100:
Options: (a) 81 (b) 90 (c) 99 (d) 96
Ans: (c)

60. Which number is divisible by 3, 5, and 7?
Options: (a) 105 (b) 70 (c) 35 (d) 140
Ans: (a)