RBSE Solutions Class 6 Maths Chapter 2 Relation Among Numbers Exercise 2.2

Rajasthan Board RBSE Class 6 Maths Chapter 2 Relation Among Numbers Ex 2.2

Question 1. Find out the prime factors of following numbers.
(i) 28
(ii) 54
(iii) 96
(iv) 148
(v) 156
Answer:
(i) To find all factors of 48:
\( 48 = 1 \times 48 \)
\( 48 = 2 \times 24 \)
\( 48 = 3 \times 16 \)
\( 48 = 4 \times 12 \)
\( 48 = 6 \times 8 \)
\( 48 = 8 \times 6 \)
All factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
(ii) To find all factors of 36:
\( 36 = 1 \times 36 \)
\( 36 = 2 \times 18 \)
\( 36 = 3 \times 12 \)
\( 36 = 4 \times 9 \)
\( 36 = 6 \times 6 \)
All factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
(iii) To find all factors of 28:
\( 28 = 1 \times 28 \)
\( 28 = 2 \times 14 \)
\( 28 = 4 \times 7 \)
\( 28 = 7 \times 4 \)
All factors of 28 are 1, 2, 4, 7, 14, and 28. Finding all factors helps you understand prime factorization better.
(iv) To find all factors of 100:
\( 100 = 1 \times 100 \)
\( 100 = 2 \times 50 \)
\( 100 = 4 \times 25 \)
\( 100 = 5 \times 20 \)
\( 100 = 10 \times 10 \)
All factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
(v) To find all factors of 125:
\( 125 = 1 \times 125 \)
\( 125 = 5 \times 25 \)
\( 125 = 25 \times 5 \)
All factors of 125 are 1, 5, 25, and 125.
In simple words: To find all factors, you list all the pairs of numbers that multiply together to give the original number. The prime factors are the prime numbers in that list.

🎯 Exam Tip: When asked for "prime factors", make sure your final answer only includes prime numbers (like 2, 3, 5, 7, etc.) that multiply to make the original number, not all factors.

Question 3. Find out common factors of the following :
(i) 24, 36
(ii) 35, 40
(iii) 12, 18, 30
(iv) 14, 25, 35
Answer:
(i) For 24 and 36:
Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
The common factors of 24 and 36 are 1, 2, 3, 4, 6, 12.
(ii) For 35 and 40:
Factors of 35 are 1, 5, 7, 35.
Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40.
The common factors of 35 and 40 are 1, 5.
(iii) For 12, 18, and 30:
Factors of 12 are 1, 2, 3, 4, 6, 12.
Factors of 18 are 1, 2, 3, 6, 9, 18.
Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
The common factors of 12, 18, and 30 are 1, 2, 3, 6.
(iv) For 14, 25, and 35:
Factors of 14 are 1, 2, 7, 14.
Factors of 25 are 1, 5, 25.
Factors of 35 are 1, 5, 7, 35.
The common factor of 14, 25, and 35 is 1. This means 1 is the only number that can divide all three without a remainder.
In simple words: Find all the numbers that can divide each number evenly. Then, look for the numbers that appear in the factor lists of all the given numbers. These are the common factors.

🎯 Exam Tip: Always list all factors for each number first, then clearly identify the common ones by circling them or listing them separately. This helps avoid mistakes and shows your working clearly.

Question 5. Write all the numbers smaller than 50, which are common multiple of 2 and 3.
Answer: The common multiples of 2 and 3 are found by listing multiples of both and finding the ones they share. Alternatively, you can find the least common multiple (LCM) first. The LCM of 2 and 3 is 6. All common multiples will be multiples of 6.
So, the common multiples of 2 and 3 that are smaller than 50 are:
6, 12, 18, 24, 30, 36, 42, 48.
In simple words: We need to find numbers under 50 that can be divided evenly by both 2 and 3. These are the numbers that are multiples of 6.

🎯 Exam Tip: To find common multiples of two numbers, first find their Least Common Multiple (LCM). Then, list the multiples of the LCM to get all common multiples. Always check the range given (e.g., "smaller than 50").