Maharashtra Board Class 6 Maths Chapter 9 HCF LCM Set 23 Solutions

Question 1. Write all the factors of the given numbers and list their common factors:
(i) 12, 16
(ii) 21, 24
(iii) 25, 30
(iv) 24, 25
(v) 56, 72
Answer:
i. Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 16 = 1, 2, 4, 8, 16
∴ Common factors of 12 and 16 = 1, 2, 4

ii. Factors of 21 = 1, 3, 7, 21
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
∴ Common factors of 21 and 24 = 1, 3

iii. Factors of 25 = 1, 5, 25
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
∴ Common factors of 25 and 30 = 1, 5

iv. Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Factors of 25 = 1,5, 25
∴ Common factor of 24 and 25 = 1

v. Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
∴ Common factors of 56 and 72 = 1, 2, 4, 8
In simple words: To find common factors, list all factors for each number and then identify the numbers that appear in both lists. This helps in understanding the shared divisors of given numbers.

🎯 Exam Tip: Always list all factors systematically for each number before identifying the common ones to avoid missing any. Organize your factors in ascending order for clarity.

Maharashtra Board Class 6 Maths Chapter 9 Hcf-Lcm Practice Set 23 Intext Questions And Activities

Question 1. In the empty boxes, write the proper words: dividend, divisor, quotient, remainder. (Textbook pg. no. 46)
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र दो दीर्घ विभाजन समस्याओं को दर्शाता है। पहली समस्या में, 36 को 4 से विभाजित किया गया है, जहाँ 4 भाजक, 36 भाज्य, 9 भागफल और 0 शेषफल है। दूसरी समस्या में, 65 को 9 से विभाजित किया गया है, जहाँ 9 भाजक, 65 भाज्य, 7 भागफल और 2 शेषफल है, और इसमें संबंधित शब्दों को खाली बक्सों में भरना है।
Answer:
When we divide 36 by 4, the remainder is zero. Therefore, 4 is a factor of 36 and 36 is a multiple of 4. But, when we divide 65 by 9, the remainder is not zero. Therefore, 9 is not a factor of 65. Also, 65 is not a multiple of 9.
In simple words: When a number divides another number with no remainder, the divisor is a factor, and the dividend is a multiple. If there's a remainder, it's neither.

🎯 Exam Tip: Clearly identify the dividend, divisor, quotient, and remainder in division problems. Understanding their roles is fundamental to concepts of factors and multiples.

Question 2. Write all the factors of the numbers 36 and 48. Also, list their common factors. (Textbook pg. no. 46)
Answer:
Solution:
36 = 1 x 36
= 2 × 18
= 3 x 12
= 4 × 9
= 6 x 6

48 = 1 x 48
= 2 × 24
= 3 x 16
= 4 × 12
= 6 x 8

∴ Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common factors of 36 and 48: [1],[2], [3], [4], [6], [12]
In simple words: To find all factors, list pairs of numbers that multiply to the given number. Then, identify the numbers that appear in the factor lists of both numbers to find their common factors.

🎯 Exam Tip: For composite numbers, systematically list factor pairs starting from 1 to ensure all factors are identified. Common factors are the intersection of these individual factor sets.