Section A – Multiple Choice Questions (1 mark each)
1. Which of the following numbers is divisible by 9?
a) 1234 b) 2349 c) 2456 d) 3332
2. The number 462 is divisible by:
a) 2 only b) 3 only c) Both 2 and 3 d) Neither
3. Which is a prime number? a) 15 b) 19 c) 21 d) 25
4. The HCF of 36 and 96 is: a) 4 b) 6 c) 12 d) 18
5. Which of the following is a composite number?
a) 2 b) 13 c) 17 d) 24
6. The LCM of 12, 36 and 60 is: a) 120 b) 240 c) 180 d) 90
7. Which of the following is NOT a multiple of 25?
a) 125 b) 225 c) 325 d) 230
8. If the HCF of two numbers is 9 and their LCM is 504, one number is 63,
then the other is: a) 72 b) 84 c) 56 d) 81
9. The product of two numbers is always equal to:
a) HCF + LCM b) HCF × LCM c) LCM – HCF d) None
Section B – Fill in the blanks (1 mark each)
10. A number is divisible by 5 if its ones digit is either ____ or ____.
11. Factors of 18 are ____.
12. Every prime number has exactly ____ factors.
13. The smallest 4-digit number divisible by 2, 3, 4, 5, and 6 is ____.
14. Numbers having no common factor other than 1 are called ____ numbers.
15. A number divisible by 10 must end with ____.
16. The factors of 20 are ____.
17. The LCM of 25 and 30 is ____.
Section C – True or False (1 mark each)
18. A number divisible by 12 must be divisible by 3 and 4. ( )
19. A number divisible by 9 is also divisible by 18. ( )
20. All even numbers are divisible by 4. ( )
21. The HCF of two numbers can never be larger than any of the given
numbers. ( )
22. Every multiple of 5 ends with 0 or 5. ( )
23. All prime numbers are odd. ( )
24. The only even prime number is 2. ( )
Section D – 2 Marks Questions
25. Check whether 12,925 is divisible by 5.
26. Find the prime factorisation of 88.
27. Write any two examples of co-prime numbers between 10 and 30.
28. Write the prime numbers between 20 and 50.
29. Replace # in 273# by the smallest digit such that the number is divisible
by 3.
30. Find the HCF of 35 and 175.
31. Write three common multiples of 15 and 25.
32. Replace # in 348# so that the number is divisible by 5 but not 10.
Section E – 3 Marks Questions
33. Find the prime factorisation of 96 using factor tree method.
34. Find the HCF of 42, 105 and 63 by prime factorisation method.
35. State whether the following pairs are co-prime or not:
a) 42 and 39
b) 19 and 23
c) 18 and 33
36. Find the LCM of 20, 25 and 30.
37. Three traffic lights change after 10 min, 15 min and 20 min. If they
change together at 9 a.m., at what time will they change together again?
Section F – 5 Marks Questions
38. Write all the factors of 24, 36 and 48. Find their HCF.
39. Find the HCF of 36, 64 and 96 using:
a) Prime factorisation method
b) Short division method
40. There are three drums containing 42, 70 and 98 litres of water. Find the
capacity of the largest container that can be used to measure water in these
drums exactly.
41. Write 16, 36, 42 and 28 as the sum of two prime numbers.
42. Verify the relation Product of two numbers = HCF × LCM for 25 and 45.
Section G – Case-based (4 Marks)
43. A farmer wants to plant sunflower plants. He wants the number of plants
in each horizontal row to be a multiple of 25 and in each vertical column a
multiple of 15. He also wants the number of rows and columns to be equal.
a) What is the least number of plants in each row and each column?
b) If he removes the first 3 rows and 2 columns of plants, how many plants
are removed?
c) If tied into bundles of 9, how many bundles are made?
Section H – Word Problems (5 Marks each)
44. Mrs. Malhotra has raised a charity fund of ₹1,97,358 equally among six
orphanages and ₹23,46,748 equally among four old-age homes. Help her to
check if she can do equal division of money.
45. Chris, Sunil and Jose were practising for a hurdle race. Chris crosses a
hurdle every 20 m, Sunil every 25 m, Jose every 30 m.
a) What is the least distance after which all of them will face a common
hurdle?
b) How many hurdles will each cross till then?
46. Find the greatest length of a scale that can be used to measure exactly
35 m and 63 m of cloth.
Section I – HOTS (6 Marks each)
47. Find the greatest number which leaves a remainder 1 when dividing 151,
a remainder 2 when dividing 127, and a remainder 3 when dividing 178.
48. Kabir has some marbles. If he arranges them in groups of 5, 4 marbles
are left. If he arranges them in groups of 4, 3 are left. If he arranges them in
groups of 3, 2 are left. If he arranges them in groups of 2, 1 is left. If the
number of marbles is less than 60, how many marbles does he have?
49. Find the greatest number that divides 149 leaving a remainder 5, and
101 leaving a remainder 5.
50. If HCF of two numbers is 9 and LCM is 504, and one number is 63, find
the other number.
51. Find the values of A and B if the number 7A579B88 is divisible by 33.
