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Question (11)

QN0030443

Find the HCF of 72 and 120.

(A) 12
(B) 18
(C) 24
(D) 36

Correct Answer: C

Explanation:

HCF = 2³ × 3 = 24.

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Question (12)

QN0030444

The HCF of 45, 60 and 75 is:

(A) 5
(B) 10
(C) 15
(D) 30

Correct Answer: C

Explanation:

Common prime factors give HCF = 3 × 5 = 15.

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Question (13)

QN0030445

The prime factorisations of two numbers are: 48 = 2 × 2 × 2 × 2 × 3 60 = 2 × 2 × 3 × 5 The HCF is:

(A) 6
(B) 12
(C) 24
(D) 60

Correct Answer: B

Explanation:

Common prime factors with minimum powers give HCF = 2² × 3 = 12.

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Question (14)

QN0030446

Which pair of numbers is co-prime?

(A) 24 and 30
(B) 25 and 36
(C) 28 and 42
(D) 27 and 45

Correct Answer: B

Explanation:

25 and 36 have no common factor other than 1.

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Question (15)

QN0030447

A rectangular garden measures 45 m by 60 m. It is to be divided into the largest possible square plots of equal size. What should be the side of each square plot?

(A) 10 m
(B) 12 m
(C) 15 m
(D) 20 m

Correct Answer: C

Explanation:

HCF of 45 and 60 is 15.

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Question (16)

QN0030448

A shopkeeper has 96 kg of rice and 144 kg of wheat. He wants to pack them in bags of equal weight without mixing them and use the fewest bags possible. What should be the weight of each bag?

(A) 12 kg
(B) 24 kg
(C) 36 kg
(D) 48 kg

Correct Answer: D

Explanation:

HCF of 96 and 144 is 48.

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Question (17)

QN0030449

The prime factorisation of a number is 2 × 2 × 3 × 5. Which of the following is NOT a factor of the number?

(A) 6
(B) 10
(C) 15
(D) 18

Correct Answer: D

Explanation:

18 requires two factors of 3, but only one is available.

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Question (18)

QN0030450

Which statement is correct while finding the HCF using prime factorisation?

(A) Include all prime factors appearing in either number.
(B) Include only the greatest prime factor.
(C) Include the common prime factors with their minimum occurrences.
(D) Include the common prime factors with their maximum occurrences.

Correct Answer: C

Explanation:

HCF is obtained using common prime factors with minimum powers.

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Question (19)

QN0030451

The prime factorisations of two numbers are: 108 = 2² × 3³ 180 = 2² × 3² × 5 The HCF is:

(A) 18
(B) 36
(C) 54
(D) 90

Correct Answer: B

Explanation:

HCF = 2² × 3² = 36.

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Question (20)

QN0030452

Two ribbons of lengths 63 cm and 81 cm are to be cut into the longest possible equal pieces without any ribbon being left over. What will be the length of each piece?

(A) 3 cm
(B) 6 cm
(C) 9 cm
(D) 27 cm

Correct Answer: C

Explanation:

HCF of 63 and 81 is 9.

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Question (11)

Find the HCF of 72 and 120.

Explanation:

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Question (12)

The HCF of 45, 60 and 75 is:

Explanation:

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Question (13)

The prime factorisations of two numbers are: 48 = 2 × 2 × 2 × 2 × 3 60 = 2 × 2 × 3 × 5 The HCF is:

Explanation:

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Question (14)

Which pair of numbers is co-prime?

Explanation:

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Question (15)

A rectangular garden measures 45 m by 60 m. It is to be divided into the largest possible square plots of equal size. What should be the side of each square plot?

Explanation:

Link:

Question (16)

A shopkeeper has 96 kg of rice and 144 kg of wheat. He wants to pack them in bags of equal weight without mixing them and use the fewest bags possible. What should be the weight of each bag?

Explanation:

Link:

Question (17)

The prime factorisation of a number is 2 × 2 × 3 × 5. Which of the following is NOT a factor of the number?

Explanation:

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Question (18)

Which statement is correct while finding the HCF using prime factorisation?

Explanation:

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Question (19)

The prime factorisations of two numbers are: 108 = 2² × 3³ 180 = 2² × 3² × 5 The HCF is:

Explanation:

Link:

Question (20)

Two ribbons of lengths 63 cm and 81 cm are to be cut into the longest possible equal pieces without any ribbon being left over. What will be the length of each piece?

Explanation:

Link:

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