RBSE Solutions Class 6 Maths Chapter 2 Relation Among Numbers Exercise 2.1

Question 1. Write all factors of the following numbers.
(i) 48
(ii) 36
(iii) 28
(iv) 100
(v) 125
Answer:
(i) For 48, we find all the numbers that divide it exactly. These are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. Factors always come in pairs that multiply to give the original number.
(ii) For 36, the factors are the numbers that can divide it without leaving a remainder. These are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Finding factors helps us understand how a number can be broken down.
(iii) For 28, we list all the whole numbers that multiply to give 28. The factors are 1, 2, 4, 7, 14, and 28.
(iv) For 100, the factors are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Numbers ending in zero often have 2, 5, and 10 as factors.
(v) For 125, the factors are 1, 5, 25, and 125. When a number ends in 5, it always has 5 as a factor.
In simple words: Factors are numbers that divide another number perfectly. You can find them by listing all pairs of numbers that multiply to give the original number.

🎯 Exam Tip: To ensure you don't miss any factors, always list them in pairs, starting from 1 and working your way up. For example, for 48: (1, 48), (2, 24), (3, 16), (4, 12), (6, 8).

Question 2. Write the first five multiples of the following numbers:
(i) 7
(ii) 12
(iii) 17
(iv) 15
(v) 18
Answer:
(i) To find the first five multiples of 7, we multiply 7 by the numbers 1, 2, 3, 4, and 5. The multiples are 7, 14, 21, 28, and 35. Multiples are like counting in steps of that number.
(ii) For 12, we multiply it by the first five counting numbers. The first five multiples are 12, 24, 36, 48, and 60. This is similar to the 12 times table.
(iii) For 17, we multiply it by 1, 2, 3, 4, and 5. The first five multiples are 17, 34, 51, 68, and 85. Multiples are numbers that can be divided exactly by the original number.
(iv) For 15, we multiply it by 1, 2, 3, 4, and 5. The first five multiples are 15, 30, 45, 60, and 75.
(v) For 18, we multiply it by 1, 2, 3, 4, and 5. The first five multiples are 18, 36, 54, 72, and 90. Multiples are formed by repeatedly adding the number to itself.
In simple words: Multiples are the answers you get when you multiply a number by whole numbers like 1, 2, 3, and so on.

🎯 Exam Tip: The first multiple of any number is always the number itself (e.g., 7 x 1 = 7). Always remember to include this when listing the first few multiples.

Question 3. Write all prime numbers between 10 and 30.
Answer: A prime number is a whole number greater than 1 that has only two factors: 1 and itself. Between 10 and 30, the prime numbers are 11, 13, 17, 19, 23, and 29. These numbers cannot be divided evenly by any other number except 1 and themselves. You can test each number to make sure it only has two factors.
In simple words: Prime numbers are special numbers that can only be split into equal groups by 1 or by themselves. Between 10 and 30, these are 11, 13, 17, 19, 23, and 29.

🎯 Exam Tip: To quickly check if a number is prime, try dividing it by small prime numbers like 2, 3, 5, 7, etc. If none of these divide it evenly, it's likely prime.

Question 4. Write the smallest prime number.
Answer: The smallest prime number is 2. It is unique because it is the only even prime number; all other even numbers can be divided by 2, making them not prime. A prime number must be greater than 1.
In simple words: The smallest prime number is 2. It's the only even number that is prime.

🎯 Exam Tip: Remember that 1 is not a prime number because it only has one factor (itself), not two distinct factors.

Question 6. Write 3 numbers which are multiples of 4 and 6.
Answer: We need to find numbers that are common multiples of both 4 and 6. This means the numbers must be divisible by both 4 and 6. Three such numbers are 12, 24, and 36. These numbers are also multiples of the least common multiple (LCM) of 4 and 6, which is 12.
In simple words: Numbers that are multiples of both 4 and 6 mean they appear in both the 4 times table and the 6 times table. Three examples are 12, 24, and 36.

🎯 Exam Tip: To find common multiples easily, start by listing the multiples of the larger number and check if they are also multiples of the smaller number.

Question 7. State whether True or False
(i) 108 is a multiple of 9.
(ii) 7 is a factor of 27.
(iii) The sum of two prime numbers is an even number.
(iv) Every prime number is odd.
(v) 1 is a factor of every number.
(vi) Multiple of each number is less than the number itself.
(vii) Factor of each number is less than the number itself.
Answer:
(i) True. When 108 is divided by 9, the answer is 12 with no remainder, meaning 108 is indeed a multiple of 9.
(ii) False. If you divide 27 by 7, you get a remainder of 6, which means 7 does not divide 27 evenly, so it's not a factor.
(iii) False. For example, 2 and 3 are prime numbers, and their sum is \( 2 + 3 = 5 \), which is an odd number. This shows the statement is not always true.
(iv) False. The number 2 is a prime number, and it is an even number. This is the only exception, making the statement false.
(v) True. Any whole number can be divided by 1, resulting in the same whole number. So, 1 is a universal factor.
(vi) False. Multiples of a number are generally greater than or equal to the number itself (e.g., multiples of 3 are 3, 6, 9,...). The only exception might be considering negative multiples, but typically multiples refer to positive integer multiples.
(vii) False. A factor of a number can be equal to the number itself. For example, the factors of 10 are 1, 2, 5, and 10. The number 10 is a factor of 10, and it is not less than 10.
In simple words: We check each statement to see if it is always true or if there is any case where it is false. Factors always divide evenly, and multiples are what you get when you multiply.

🎯 Exam Tip: For True/False questions, especially in maths, try to think of counterexamples. If you can find just one case where the statement is false, then the entire statement is false.