Chapter Exam

Chapter-11 Finding Common Ground — Online MCQ Test

Q: What is the full form of HCF?

Answer: A. Highest Common Factor — HCF stands for Highest Common Factor, which is the largest number that divides two or more numbers without leaving a remainder.

Q: What is the full form of LCM?

Answer: A. Least Common Multiple — LCM stands for Least Common Multiple, which is the smallest number that is a multiple of two or more given numbers.

Q: Which of the following is a factor of 24?

Answer: C. 8 — A factor of 24 is a number that divides 24 completely. 24 ÷ 8 = 3, so 8 is a factor of 24.

Q: Which of the following is a multiple of 6?

Answer: B. 24 — A multiple of 6 is obtained by multiplying 6 by a whole number. 6 × 4 = 24, so 24 is a multiple of 6.

Q: Find the HCF of 15 and 25 using prime factorization.

Answer: B. 5 — 15 = 3 × 5 and 25 = 5 × 5. The common prime factor is 5, so HCF = 5.

Q: Find the LCM of 8 and 12 using prime factorization.

Answer: A. 24 — 8 = 2³ and 12 = 2² × 3. LCM = 2³ × 3 = 8 × 3 = 24.

Q: Compare: HCF(12, 18) ___ HCF(15, 25)

Answer: A. Greater than — HCF(12, 18) = 6 and HCF(15, 25) = 5. Since 6 > 5, HCF(12, 18) is greater than HCF(15, 25).

Q: The HCF of two consecutive even numbers is always ___.

Answer: B. 2 — Consecutive even numbers like 4 and 6, or 8 and 10, always have HCF = 2 because they share only 2 as a common factor.

Q: The factors of 28 are 1, 2, 4, 7, 14, 28. The sum of all factors is ___.

Answer: A. 56 — Sum = 1 + 2 + 4 + 7 + 14 + 28 = 56. This is a direct calculation of the sum of all factors.

Q: Which set of numbers has LCM = 60 and HCF = 6?

Answer: C. 6, 12, 60 — For 6, 12, 60: Factors of 6={1,2,3,6}, 12={1,2,3,4,6,12}, 60={1,2,3,4,5,6,10,12,15,20,30,60}. HCF=6, LCM=60. This is correct.

MATHS · Grade 7 · CBSE(NCERT)

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Chapter-11 Finding Common Ground — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 7 MATHS — Chapter-11 Finding Common Ground, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the full form of HCF?

A. Highest Common Factor ✓
B. Highest Common Figure
C. High Calculation Formula
D. Horizontal Common Factor

Answer: A. Highest Common Factor
HCF stands for Highest Common Factor, which is the largest number that divides two or more numbers without leaving a remainder.

What is the full form of LCM?

A. Least Common Multiple ✓
B. Large Common Multiple
C. Lowest Calculation Method
D. Least Common Measure

Answer: A. Least Common Multiple
LCM stands for Least Common Multiple, which is the smallest number that is a multiple of two or more given numbers.

Which of the following is a factor of 24?

A. 5
B. 7
C. 8 ✓
D. 11

Answer: C. 8
A factor of 24 is a number that divides 24 completely. 24 ÷ 8 = 3, so 8 is a factor of 24.

Which of the following is a multiple of 6?

A. 16
B. 24 ✓
C. 25
D. 35

Answer: B. 24
A multiple of 6 is obtained by multiplying 6 by a whole number. 6 × 4 = 24, so 24 is a multiple of 6.

Find the HCF of 15 and 25 using prime factorization.

A. 3
B. 5 ✓
C. 15
D. 75

Answer: B. 5
15 = 3 × 5 and 25 = 5 × 5. The common prime factor is 5, so HCF = 5.

Find the LCM of 8 and 12 using prime factorization.

A. 24 ✓
B. 48
C. 96
D. 20

Answer: A. 24
8 = 2³ and 12 = 2² × 3. LCM = 2³ × 3 = 8 × 3 = 24.

Compare: HCF(12, 18) ___ HCF(15, 25)

A. Greater than ✓
B. Less than
C. Equal to
D. Cannot be determined

Answer: A. Greater than
HCF(12, 18) = 6 and HCF(15, 25) = 5. Since 6 > 5, HCF(12, 18) is greater than HCF(15, 25).

The HCF of two consecutive even numbers is always ___.

A. 1
B. 2 ✓
C. 4
D. Depends on the numbers

Answer: B. 2
Consecutive even numbers like 4 and 6, or 8 and 10, always have HCF = 2 because they share only 2 as a common factor.

The factors of 28 are 1, 2, 4, 7, 14, 28. The sum of all factors is ___.

A. 56 ✓
B. 42
C. 48
D. 112

Answer: A. 56
Sum = 1 + 2 + 4 + 7 + 14 + 28 = 56. This is a direct calculation of the sum of all factors.

Which set of numbers has LCM = 60 and HCF = 6?

A. 6, 12, 30
B. 12, 20, 30
C. 6, 12, 60 ✓
D. 10, 12, 60

Answer: C. 6, 12, 60
For 6, 12, 60: Factors of 6={1,2,3,6}, 12={1,2,3,4,6,12}, 60={1,2,3,4,5,6,10,12,15,20,30,60}. HCF=6, LCM=60. This is correct.

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