RBSE Solutions Class 6 Maths Chapter 2 Relation Among Numbers Important Questions

Multiple Choice Questions

 

Question 1. Factors of number 24 are :
(i) 1, 2, 3
(ii) 4, 6
(iii) 12, 24
(iv) All of the options
Answer: (iv) All of the options
In simple words: The numbers that divide 24 exactly are 1, 2, 3, 4, 6, 8, 12, and 24. So, all the options listed are correct parts of the factors.

🎯 Exam Tip: To find factors, try dividing the number by integers from 1 up to its square root. If 'a' is a factor, then 'number/a' is also a factor.

 

Question 2. Number of prime numbers between 1 to 100 are:
(i) 24
(ii) 25
(iii) 26
(iv) 27
Answer: (ii) 25
In simple words: Between the numbers 1 and 100, there are 25 special numbers called prime numbers. These numbers can only be divided by 1 and by themselves.

🎯 Exam Tip: Memorizing the count of prime numbers up to 50 or 100 can save time in MCQ exams.

 

Question 3. Number which is not divisible by 2 :
(i) 267
(ii) 468
(iii) 192
(iv) 374
Answer: (i) 267
In simple words: Numbers that end with 0, 2, 4, 6, or 8 can be divided by 2. The number 267 ends with 7, so it cannot be divided by 2.

🎯 Exam Tip: To check divisibility by 2, only look at the last digit of the number.

 

Question 4. First three multiples of 15 are :
(i) 15, 30, 60
(ii) 15, 45, 60
(iii) 15, 30, 45
(iv) None of the options
Answer: (iii) 15, 30, 45
In simple words: Multiples are what you get when you multiply a number by other whole numbers. So, for 15, the first three multiples are 15 (15x1), 30 (15x2), and 45 (15x3).

🎯 Exam Tip: Remember that the first multiple of any number is always the number itself.

 

Question 6. L.C.M. of 40, 15, 20 is :
(i) 120
(ii) 100
(iii) 140
(iv) 160
Answer: (i) 120
In simple words: The LCM is the smallest number that 40, 15, and 20 can all divide into without leaving a remainder. We find it by breaking down each number into its prime parts and then multiplying the highest powers of all these parts.

🎯 Exam Tip: For LCM, take the highest power of each prime factor that appears in any of the numbers.

 

Question 7. Common factor of 18, 27 is :
(i) 2
(ii) 4
(iii) 6
(iv) 9
Answer: (iv) 9
In simple words: A common factor is a number that can divide two or more numbers perfectly. For 18 and 27, numbers like 1, 3, and 9 are common factors. From the choices, 9 is the largest common factor.

🎯 Exam Tip: When finding common factors, list all factors of each number first, then pick out the ones that appear in every list.

 

Question 8. Prime number in the following is :
(i) 6
(ii) 7
(iii) 9
(iv) 10
Answer: (ii) 7
In simple words: A prime number is a special number that only has two ways to be divided: by 1, or by itself. Out of the given numbers, only 7 fits this rule.

🎯 Exam Tip: Remember that 1 is not a prime number. The smallest prime number is 2, and it is the only even prime number.

Fill In The Blanks

 

Question (i) Reverse process of factors is called ..........
Answer: expansion
In simple words: When you find factors, you break a number down. The opposite is like building it up, which is called expansion or finding multiples.

🎯 Exam Tip: Understanding the relationship between factors and multiples helps in solving many number system problems.

 

Question (ii) The numbers having more than two factors are called ..........
Answer: composite
In simple words: If a number can be divided by more than just 1 and itself, it is called a composite number.

🎯 Exam Tip: All whole numbers greater than 1 are either prime or composite.

 

Question (iii) ............ is even prime number.
Answer: 2
In simple words: The number 2 is special because it's the only even number that is also a prime number. All other even numbers can be split into smaller numbers.

🎯 Exam Tip: Always remember that 2 is the smallest and only even prime number.

 

Question (iv) The numbers completely divisible by 2 are called ..........
Answer: even
In simple words: Numbers that you can divide by 2 perfectly, with no leftover, are called even numbers. They always end with a 0, 2, 4, 6, or 8.

🎯 Exam Tip: The divisibility rule for 2 is one of the simplest and most frequently used.

 

Question (v) Multiples of same multiple numbers are called ..........
Answer: common factor
In simple words: A common factor is a number that can divide two or more other numbers without any leftover.

🎯 Exam Tip: A common factor is a number that divides two or more numbers perfectly. Do not confuse it with common multiples.

 

Question (vi) Smallest odd prime number is ..........
Answer: 3
In simple words: The smallest prime number that is also an odd number is 3. Remember, 1 is not prime, and 2 is prime but it is even.

🎯 Exam Tip: Make sure to distinguish between prime, composite, even, and odd numbers.

Very Short Answer Type Questions

 

Question 1. Write all factors of 38.
Answer: To find all factors of 38, we look for pairs of numbers that multiply to give 38. These pairs are \( 1 \times 38 \) and \( 2 \times 19 \). Therefore, the factors of 38 are 1, 2, 19, and 38. Factors are numbers that divide another number exactly.
In simple words: Factors are numbers that can divide another number perfectly. For 38, the numbers that divide it exactly are 1, 2, 19, and 38.

🎯 Exam Tip: Always list factors in ascending order, starting from 1 and ending with the number itself.

 

Question 2. Write first seven multiples of 4.
Answer: The multiples of a number are the results you get when you multiply that number by counting numbers (1, 2, 3, and so on). The first seven multiples of 4 are found by multiplying 4 by 1, 2, 3, 4, 5, 6, and 7. These are 4, 8, 12, 16, 20, 24, and 28.
In simple words: To find the first seven multiples of 4, you multiply 4 by 1, then by 2, then by 3, and so on, up to 7. This gives you 4, 8, 12, 16, 20, 24, and 28.

🎯 Exam Tip: The 'n-th' multiple of a number is simply the number multiplied by 'n'.

 

Question 3. Write all prime numbers between 1 and 50.
Answer: Prime numbers are whole numbers greater than 1 that have only two factors: 1 and the number itself. Between 1 and 50, these special numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47. Each of these numbers can only be divided by 1 and itself without a remainder.
In simple words: Prime numbers are numbers bigger than 1 that only 1 and themselves can divide. From 1 to 50, these are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.

🎯 Exam Tip: A common way to find prime numbers is using the Sieve of Eratosthenes to eliminate composite numbers.

 

Question 4. Find common factors of 15, 25, 35 and 45.
Answer: To find the common factors of 15, 25, 35, and 45, we first list the prime factors for each number.
\( 15 = 1 \times 3 \times 5 \)
\( 25 = 1 \times 5 \times 5 \)
\( 35 = 1 \times 5 \times 7 \)
\( 45 = 1 \times 3 \times 3 \times 5 \)
The numbers that appear in the prime factorization of all these numbers are 1 and 5. So, the common factors are 1 and 5. These are the numbers that can divide all four given numbers without leaving a remainder.
In simple words: We find all the numbers that can divide 15, 25, 35, and 45 perfectly. By breaking them into their smallest prime parts, we see that only 1 and 5 are common to all of them.

🎯 Exam Tip: Always include 1 as a common factor unless explicitly stated otherwise, as 1 is a factor of every number.

Short/Long Answer Type Questions

 

Question 1. Test divisibility of 585 by 3, without division.
Answer: To test if 585 is divisible by 3 without actual division, we sum its digits. The sum of the digits in 585 is \( 5 + 8 + 5 = 18 \).
\( \implies \) Then, we sum the digits of 18, which is \( 1 + 8 = 9 \).
\( \implies \) Since 9 is clearly divisible by 3, the original number 585 is also divisible by 3. This rule works because of how our number system is structured.
In simple words: To check if 585 can be divided by 3, add up its digits: \( 5+8+5=18 \). Then add the digits of 18: \( 1+8=9 \). Since 9 can be divided by 3, 585 can also be divided by 3.

🎯 Exam Tip: The divisibility rule for 3 is to sum the digits; if the sum is divisible by 3, the number itself is divisible by 3.

 

Question 3. Three containers contains 26 l, 65 litre 117 l milk respectively. Find maximum measurement of container milk of all three containers.
Answer: To find the maximum measurement of a container that can exactly measure the milk from all three containers (26 l, 65 l, and 117 l), we need to find the Highest Common Factor (HCF) of these three numbers.
First, we find the prime factors:
\( 26 = 2 \times 13 \)
\( 65 = 5 \times 13 \)
\( 117 = 3 \times 3 \times 13 \)
The only common prime factor among 26, 65, and 117 is 13. Therefore, the HCF is 13. This means a container of 13 litres is the largest possible size that can measure the milk in each of the three containers perfectly.
In simple words: We want to find the biggest bucket size that can fill up the 26-litre, 65-litre, and 117-litre containers perfectly without any milk left over. To do this, we find the biggest number that divides all three milk amounts. That number is 13 litres.

🎯 Exam Tip: "Maximum measurement" or "largest container" often implies finding the HCF, while "smallest number" or "least common" suggests finding the LCM.

 

Question 4. Find the smallest number which is completely divisible by 18, 36, 50.
Answer: To find the smallest number that is completely divisible by 18, 36, and 50, we need to calculate their Least Common Multiple (LCM). We use the prime factorization method:
First, divide by common prime factors starting from 2.
Continue dividing until all numbers become 1.
Multiplying all the prime divisors gives the LCM.

\( \implies \) The LCM of 18, 36, and 50 is \( 2 \times 2 \times 3 \times 3 \times 5 \times 5 = 900 \). This number is the smallest positive integer that can be divided by 18, 36, and 50 without leaving a remainder.
In simple words: We need to find the smallest number that 18, 36, and 50 can all divide into perfectly. We do this by finding their Least Common Multiple (LCM). By dividing them all by prime numbers until we reach 1, we find the LCM is 900.

🎯 Exam Tip: Always perform the prime factorization carefully, ensuring all prime factors are included in the LCM calculation.