7TH NUMBERS FACTORS AND MULTIPLES - 5

Factors & Multiples Aptitude Quiz

1. Which of the following numbers is NOT a factor of 48?

A) 6 B) 8 C) 9 D) 12

Correct Answer: C) 9

Explanation: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. Dividing 48 by 9 leaves a remainder of 3, which means 9 is not a factor of 48.

2. What is the Least Common Multiple (LCM) of 12 and 18?

A) 36 B) 54 C) 72 D) 24

Correct Answer: A) 36

Explanation: Multiples of 12 = 12, 24, 36, 48... Multiples of 18 = 18, 36, 54... The smallest common multiple among both lists is 36.

3. What is the Highest Common Factor (HCF) of 36, 60, and 84?

A) 6 B) 12 C) 18 D) 24

Correct Answer: B) 12

Explanation: Prime factorizations:
36 = 2² × 3²
60 = 2² × 3 × 5
84 = 2² × 3 × 7
HCF is the product of common prime factors with lowest powers: 2² × 3 = 12.

4. Find the smallest 3-digit number that is a multiple of both 6 and 9.

A) 102 B) 108 C) 114 D) 126

Correct Answer: B) 108

Explanation: First find LCM(6, 9) = 18. Multiples of 18 are 18, 36, 54, 72, 90, 108, 126... The first 3-digit multiple is 108.

5. What is the total number of positive factors for 72?

A) 8 B) 10 C) 12 D) 14

Correct Answer: C) 12

Explanation: 72 = 2³ × 3². Using the factor formula (p+1)(q+1)... total factors = (3+1)(2+1) = 4 × 3 = 12 factors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72).

6. Three bells toll together at intervals of 9, 12, and 15 minutes respectively. If they toll together now, after how many hours will they toll together next?

A) 2 hours B) 3 hours C) 4 hours D) 5 hours

Correct Answer: B) 3 hours

Explanation: Find the LCM of 9, 12, and 15.
LCM(9, 12, 15) = 180 minutes.
Convert to hours: 180 ÷ 60 = 3 hours.

7. A gardener wants to plant 48 rose plants and 72 jasmine plants in equal rows such that each row contains only one type of plant. What is the maximum number of plants that can be put in each row?

A) 12 B) 16 C) 24 D) 36

Correct Answer: C) 24

Explanation: Finding the maximum equal division requires calculating the HCF of 48 and 72.
HCF(48, 72) = 24.

8. Priya has a piece of cloth measuring 105 cm by 135 cm. She wants to cut it into equal square pieces without leftover cloth. What is the side length of the largest square piece she can cut?

A) 5 cm B) 15 cm C) 25 cm D) 35 cm

Correct Answer: B) 15 cm

Explanation: The largest side length of the square piece corresponds to the HCF of 105 and 135.
105 = 3 × 5 × 7
135 = 3³ × 5
HCF = 3 × 5 = 15 cm.

9. Rahul and Anita start running around a circular track at the same time. Rahul completes a round in 24 seconds, while Anita takes 36 seconds. After how many seconds will they meet again at the starting point?

A) 72 seconds B) 108 seconds C) 144 seconds D) 48 seconds

Correct Answer: A) 72 seconds

Explanation: To find when they meet at the starting point simultaneously, calculate LCM(24, 36).
24 = 2³ × 3
36 = 2² × 3²
LCM = 2³ × 3² = 72 seconds.

10. What is the smallest number which when divided by 12, 16, and 24 leaves a remainder of 5 in each case?

A) 43 B) 48 C) 53 D) 96

Correct Answer: C) 53

Explanation: The required number is LCM(12, 16, 24) + Remainder.
LCM(12, 16, 24) = 48.
48 + 5 = 53.

11. If A and B are two prime numbers, what is their HCF and LCM respectively?

A) HCF = 1, LCM = A + B B) HCF = 0, LCM = A × B C) HCF = 1, LCM = A × B D) HCF = A, LCM = B

Correct Answer: C) HCF = 1, LCM = A × B

Explanation: Since prime numbers share no common factors other than 1, their HCF is always 1 and their LCM is their direct product (A × B).

12. The HCF of two numbers is 16 and their product is 3072. What is their LCM?

A) 192 B) 256 C) 384 D) 512

Correct Answer: A) 192

Explanation: Apply the formula: HCF × LCM = Product of the two numbers.
16 × LCM = 3072
LCM = 3072 ÷ 16 = 192.

13. Find the sum of all prime factors of 210.

A) 15 B) 17 C) 19 D) 21

Correct Answer: B) 17

Explanation: Prime factors of 210 = 2 × 3 × 5 × 7.
Sum of prime factors = 2 + 3 + 5 + 7 = 17.

14. Traffic lights at three crossings change after 48 sec, 72 sec, and 108 sec respectively. If they change together at 8:00:00 AM, when will they change together next?

A) 8:07:12 AM B) 8:08:20 AM C) 8:06:12 AM D) 8:10:00 AM

Correct Answer: A) 8:07:12 AM

Explanation: LCM(48, 72, 108) = 432 seconds.
432 seconds = 7 minutes and 12 seconds.
Next simultaneous change = 8:00:00 AM + 7 min 12 sec = 8:07:12 AM.

15. What is the greatest 4-digit number that is exactly divisible by 15, 20, and 25?

A) 9900 B) 9960 C) 9930 D) 9850

Correct Answer: A) 9900

Explanation: LCM(15, 20, 25) = 300.
The largest 4-digit number is 9999.
9999 ÷ 300 = 33 with a remainder of 99.
Required number = 9999 - 99 = 9900.