Default Title

Question (11)

QN0036482

Find the HCF of 144 and 180.

(A) 18
(B) 24
(C) 36
(D) 48

Correct Answer: C

Explanation:

144 = 2⁴ × 3² and 180 = 2² × 3² × 5. Hence HCF = 2² × 3² = 36.

Link:

Report Error

Question (12)

QN0036483

Find the LCM of 24, 36 and 54.

(A) 108
(B) 216
(C) 324
(D) 432

Correct Answer: B

Explanation:

24 = 2³ × 3, 36 = 2² × 3² and 54 = 2 × 3³. Therefore, LCM = 2³ × 3³ = 216.

Link:

Report Error

Question (13)

QN0036484

Two numbers have prime factorisations 2³ × 3² and 2² × 3³. Their HCF is:

(A) 2² × 3²
(B) 2³ × 3³
(C) 2² × 3³
(D) 2³ × 3²

Correct Answer: A

Explanation:

For HCF, take the smallest power of each common prime. Thus HCF = 2² × 3².

Link:

Report Error

Question (14)

QN0036485

For the same two numbers 2³ × 3² and 2² × 3³, their LCM is:

(A) 2² × 3²
(B) 2³ × 3²
(C) 2² × 3³
(D) 2³ × 3³

Correct Answer: D

Explanation:

For LCM, take the greatest power of every prime involved. Thus LCM = 2³ × 3³ = 216.

Link:

Report Error

Question (15)

QN0036486

Which number cannot be expressed as a product of two or more prime numbers?

(A) 49
(B) 51
(C) 53
(D) 55

Correct Answer: C

Explanation:

53 is a prime number, whereas 49, 51 and 55 are composite.

Link:

Report Error

Question (16)

QN0036487

The HCF of two numbers is 16 and their LCM is 240. If one number is 48, the other number is:

(A) 60
(B) 70
(C) 80
(D) 90

Correct Answer: C

Explanation:

Product of the numbers = HCF × LCM = 16 × 240 = 3840. Other number = 3840/48 = 80.

Link:

Report Error

Question (17)

QN0036488

Three bells ring at intervals of 12, 18 and 30 minutes. If they ring together initially, after how many minutes will they next ring together?

(A) 90
(B) 120
(C) 150
(D) 180

Correct Answer: D

Explanation:

LCM of 12, 18 and 30 = 2² × 3² × 5 = 180 minutes.

Link:

Report Error

Question (18)

QN0036489

A number has prime factorisation 2⁵ × 3² × 7. How many distinct prime factors does it have?

(A) 3
(B) 4
(C) 7
(D) 56

Correct Answer: A

Explanation:

The distinct prime factors are 2, 3 and 7. Hence there are 3 distinct prime factors.

Link:

Report Error

Question (19)

QN0036490

How many factors of 360 are divisible by both 2 and 3?

(A) 6
(B) 8
(C) 12
(D) 18

Correct Answer: C

Explanation:

360 = 2³ × 3² × 5. A factor divisible by both 2 and 3 must contain at least 2¹ and 3¹. The number of choices is 3 × 2 × 2 = 12.

Link:

Report Error

Question (20)

QN0036491

If N = 2⁵ × 3² × 5, which of the following is definitely a divisor of N?

(A) 72
(B) 90
(C) 144
(D) 200

Correct Answer: B

Explanation:

90 = 2 × 3² × 5, and all these prime powers are present in N.

Link:

Report Error

Question (11)

Find the HCF of 144 and 180.

Explanation:

Link:

Question (12)

Find the LCM of 24, 36 and 54.

Explanation:

Link:

Question (13)

Two numbers have prime factorisations 2³ × 3² and 2² × 3³. Their HCF is:

Explanation:

Link:

Question (14)

For the same two numbers 2³ × 3² and 2² × 3³, their LCM is:

Explanation:

Link:

Question (15)

Which number cannot be expressed as a product of two or more prime numbers?

Explanation:

Link:

Question (16)

The HCF of two numbers is 16 and their LCM is 240. If one number is 48, the other number is:

Explanation:

Link:

Question (17)

Three bells ring at intervals of 12, 18 and 30 minutes. If they ring together initially, after how many minutes will they next ring together?

Explanation:

Link:

Question (18)

A number has prime factorisation 2⁵ × 3² × 7. How many distinct prime factors does it have?

Explanation:

Link:

Question (19)

How many factors of 360 are divisible by both 2 and 3?

Explanation:

Link:

Question (20)

If N = 2⁵ × 3² × 5, which of the following is definitely a divisor of N?

Explanation:

Link:

Excel With Tutors

ExcelWithTutors

For Student

For Tutors

Learn

OUR POLICY