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Question (31)

QN0030463

A farmer has 64 mangoes and 80 oranges. He wants to pack them into identical baskets without mixing the fruits and without any fruit left over. What is the maximum number of fruits in each basket?

(A) 8
(B) 12
(C) 16
(D) 20

Correct Answer: C

Explanation:

HCF of 64 and 80 is 16.

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Question (32)

QN0030464

The prime factorisations of two numbers are: 72 = 2³ × 3² 90 = 2 × 3² × 5 The HCF is:

(A) 6
(B) 9
(C) 18
(D) 36

Correct Answer: C

Explanation:

Common primes with minimum powers: 2 × 3² = 18.

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Question (33)

QN0030465

The HCF of two co-prime numbers is always:

(A) 0
(B) 1
(C) The smaller number
(D) The larger number

Correct Answer: B

Explanation:

Co-prime numbers have only one common factor, which is 1.

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Question (34)

QN0030466

Find the HCF of 112 and 84.

(A) 14
(B) 21
(C) 28
(D) 56

Correct Answer: C

Explanation:

HCF = 2² × 7 = 28.

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Question (35)

QN0030467

Which statement is true about finding the HCF by prime factorisation?

(A) Multiply all the prime factors of both numbers.
(B) Take only the largest prime factor.
(C) Use only the common prime factors with the least number of occurrences.
(D) Use every prime factor with the greatest number of occurrences.

Correct Answer: C

Explanation:

HCF is obtained using common prime factors with minimum powers.

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Question (36)

QN0030468

Two ropes are 56 m and 72 m long. They are cut into equal longest possible pieces without any rope being left. What will be the length of each piece?

(A) 4 m
(B) 6 m
(C) 8 m
(D) 14 m

Correct Answer: C

Explanation:

HCF of 56 and 72 is 8.

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Question (37)

QN0030469

Which of the following numbers is NOT a factor of 840?

(A) 28
(B) 30
(C) 35
(D) 45

Correct Answer: D

Explanation:

840 = 2³ × 3 × 5 × 7. 45 = 3² × 5 is not a factor.

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Question (38)

QN0030470

The HCF of 24, 36 and 60 is:

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

Correct Answer: B

Explanation:

Common prime factors give HCF = 12.

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Question (39)

QN0030471

A carpenter has wooden planks of lengths 96 cm and 120 cm. He wants to cut them into equal longest possible pieces. What will be the length of each piece?

(A) 12 cm
(B) 18 cm
(C) 24 cm
(D) 30 cm

Correct Answer: C

Explanation:

HCF of 96 and 120 is 24.

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Question (40)

QN0030472

Which of the following statements is correct?

(A) Every common factor of two numbers is greater than their HCF.
(B) The HCF is one of the common factors and is the greatest among them.
(C) Every factor of one number is also a factor of the other number.
(D) The HCF is always equal to the product of the two numbers.

Correct Answer: B

Explanation:

The HCF is the greatest among all the common factors.

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Question (31)

A farmer has 64 mangoes and 80 oranges. He wants to pack them into identical baskets without mixing the fruits and without any fruit left over. What is the maximum number of fruits in each basket?

Explanation:

Link:

Question (32)

The prime factorisations of two numbers are: 72 = 2³ × 3² 90 = 2 × 3² × 5 The HCF is:

Explanation:

Link:

Question (33)

The HCF of two co-prime numbers is always:

Explanation:

Link:

Question (34)

Find the HCF of 112 and 84.

Explanation:

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Question (35)

Which statement is true about finding the HCF by prime factorisation?

Explanation:

Link:

Question (36)

Two ropes are 56 m and 72 m long. They are cut into equal longest possible pieces without any rope being left. What will be the length of each piece?

Explanation:

Link:

Question (37)

Which of the following numbers is NOT a factor of 840?

Explanation:

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Question (38)

The HCF of 24, 36 and 60 is:

Explanation:

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Question (39)

A carpenter has wooden planks of lengths 96 cm and 120 cm. He wants to cut them into equal longest possible pieces. What will be the length of each piece?

Explanation:

Link:

Question (40)

Which of the following statements is correct?

Explanation:

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