Q.1 Which of the following is a factor of 36?
7
9
11
13
Explanation - A factor divides a number exactly. 36 ÷ 9 = 4, so 9 is a factor of 36.
Correct answer is: 9
Q.2 What is the least common multiple (LCM) of 4 and 6?
8
10
12
24
Explanation - Multiples of 4 are 4, 8, 12; multiples of 6 are 6, 12. The smallest common multiple is 12.
Correct answer is: 12
Q.3 Which number is a multiple of both 5 and 7?
20
25
35
50
Explanation - Multiples of 5 are 5, 10, 15, … and of 7 are 7, 14, 21, 28, 35. The first common multiple is 35.
Correct answer is: 35
Q.4 How many factors does 18 have?
4
5
6
8
Explanation - Factors of 18 are 1, 2, 3, 6, 9, 18. So, 6 factors in total.
Correct answer is: 6
Q.5 What is the greatest common divisor (GCD) of 20 and 28?
2
4
6
8
Explanation - Factors of 20 are 1, 2, 4, 5, 10, 20. Factors of 28 are 1, 2, 4, 7, 14, 28. Common factors: 1, 2, 4. Greatest is 4.
Correct answer is: 4
Q.6 Which of the following is NOT a factor of 48?
12
16
18
24
Explanation - 48 ÷ 18 is not an integer, so 18 is not a factor of 48.
Correct answer is: 18
Q.7 The LCM of 8 and 12 is:
16
24
36
48
Explanation - Multiples of 8: 8, 16, 24, 32…; multiples of 12: 12, 24, 36… First common multiple is 24.
Correct answer is: 24
Q.8 Which number is divisible by both 9 and 12?
36
45
54
60
Explanation - LCM of 9 and 12 is 36. So 36 is divisible by both.
Correct answer is: 36
Q.9 What is the highest factor of 50, excluding 50 itself?
10
25
20
30
Explanation - Factors of 50: 1, 2, 5, 10, 25, 50. Excluding 50, the highest is 25.
Correct answer is: 25
Q.10 Which of the following numbers is prime?
21
29
33
39
Explanation - 29 has only two factors: 1 and itself, so it is prime.
Correct answer is: 29
Q.11 The common factors of 18 and 24 are:
1, 2, 3, 6
2, 4, 8
1, 2, 5
2, 3, 12
Explanation - Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common: 1, 2, 3, 6.
Correct answer is: 1, 2, 3, 6
Q.12 What is the least common multiple of 15 and 20?
30
45
60
75
Explanation - Multiples of 15: 15, 30, 45, 60… Multiples of 20: 20, 40, 60… First common multiple is 60.
Correct answer is: 60
Q.13 How many prime factors does 60 have?
2
3
4
5
Explanation - Prime factorization of 60 = 2 × 2 × 3 × 5. The distinct prime factors are 2, 3, and 5 (3 primes).
Correct answer is: 3
Q.14 Which is the largest prime factor of 84?
3
5
7
11
Explanation - Prime factorization of 84 = 2 × 2 × 3 × 7. Largest prime factor is 7.
Correct answer is: 7
Q.15 If a number is divisible by 2 and 3, it must also be divisible by:
5
6
9
12
Explanation - A number divisible by both 2 and 3 is always divisible by their LCM, which is 6.
Correct answer is: 6
Q.16 What is the sum of all factors of 12?
20
24
28
30
Explanation - Factors of 12 are 1, 2, 3, 4, 6, 12. Their sum is 28.
Correct answer is: 28
Q.17 Which of the following is a common multiple of 9 and 15?
30
45
60
75
Explanation - Multiples of 9: 9, 18, 27, 36, 45… Multiples of 15: 15, 30, 45… First common multiple is 45.
Correct answer is: 45
Q.18 What is the GCD of 56 and 72?
4
6
8
12
Explanation - Factors of 56: 1,2,4,7,8,14,28,56. Factors of 72: 1,2,3,4,6,8,9,12,18,24,36,72. Common factors include 1,2,4,8. Greatest is 8.
Correct answer is: 8
Q.19 Which of these numbers has exactly 2 factors?
6
7
9
12
Explanation - Numbers with exactly 2 factors are primes. 7 is prime with factors 1 and 7.
Correct answer is: 7
Q.20 What is the smallest number divisible by 8, 10, and 12?
120
240
360
480
Explanation - LCM of 8, 10, 12 is 120.
Correct answer is: 120
Q.21 The product of the greatest common divisor and least common multiple of 9 and 12 equals:
36
72
108
144
Explanation - GCD(9,12)=3, LCM(9,12)=36. Their product is 3 × 36 = 108.
Correct answer is: 108
Q.22 Which of the following is a factor of both 42 and 63?
6
7
9
14
Explanation - Factors of 42: 1,2,3,6,7,14,21,42. Factors of 63: 1,3,7,9,21,63. Common factors: 1,3,7,21. Smallest listed is 7.
Correct answer is: 7
Q.23 The number of multiples of 7 between 1 and 50 is:
6
7
8
9
Explanation - Multiples of 7 up to 50 are 7,14,21,28,35,42,49. There are 7 multiples.
Correct answer is: 7
Q.24 Which is the least common multiple of 25 and 30?
50
75
150
300
Explanation - Prime factors: 25 = 5², 30 = 2 × 3 × 5. LCM = 2 × 3 × 5² = 150.
Correct answer is: 150
Q.25 What is the greatest common divisor of 81 and 108?
9
18
27
36
Explanation - Prime factors: 81 = 3⁴, 108 = 2² × 3³. GCD = 3³ = 27.
Correct answer is: 27