Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 6th

# Tamil Nadu Board Samacheer Kalvi solutions for Class 6th Mathematics Term 2 Answers Guide chapter 1 - Numbers [Latest edition]

#### Chapters ## Chapter 1: Numbers

Exercise 1.1Exercise 1.2Exercise 1.3
Exercise 1.1 [Pages 11 - 12]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 6th Mathematics Term 2 Answers Guide Chapter 1 NumbersExercise 1.1 [Pages 11 - 12]

#### Fill in the blanks

Exercise 1.1 | Q 1. (i) | Page 11

The number of prime numbers between 11 and 60 is _________

Exercise 1.1 | Q 1. (ii) | Page 11

The numbers 29 and ________ are twin primes

Exercise 1.1 | Q 1. (iii) | Page 11

3753 is divisible by 9 and hence divisible by _________

Exercise 1.1 | Q 1. (iv) | Page 11

The number of distinct prime factors of the smallest 4 digit number is __________

Exercise 1.1 | Q 1. (v) | Page 11

The sum of distinct prime factors of 30 is ________

#### Say True or False

Exercise 1.1 | Q 2. (i) | Page 11

The sum of any number of odd numbers is always even

• True

• False

Exercise 1.1 | Q 2. (ii) | Page 11

Every natural number is either prime or composite

• True

• False

Exercise 1.1 | Q 2. (iii) | Page 11

If a number is divisible by 6, then it must be divisible by 3

• True

• False

Exercise 1.1 | Q 2. (iv) | Page 11

16254 is divisible by each of 2, 3, 6 and 9

• True

• False

Exercise 1.1 | Q 2. (v) | Page 11

The number of distinct prime factors of 105 is 3

• True

• False

Exercise 1.1 | Q 3 | Page 11

Write the smallest and the biggest two digit prime number

Exercise 1.1 | Q 4 | Page 11

Write the smallest and the biggest three digit composite number

Exercise 1.1 | Q 5 | Page 11

The sum of any three odd natural numbers is odd. Justify this statement with an example

Exercise 1.1 | Q 6 | Page 11

The digits of the prime number 13 can be reversed to get another prime number 31. Find if any such pairs exist upto 100

Exercise 1.1 | Q 7 | Page 11

Your friend says that every odd number is prime. Give an example to prove him/her wrong

Exercise 1.1 | Q 8 | Page 11

Each of the composite numbers has atleast three factors. Justify this statement with an example.

Exercise 1.1 | Q 9 | Page 11

Find the dates of any month in a calendar which are divisible by both 2 and 3.

Exercise 1.1 | Q 10 | Page 11

I am a two digit prime number and the sum of my digits is 10. I am also one of the factors of 57. Who am I?

Exercise 1.1 | Q 11. a) | Page 11

Find the prime factorisation number by factor tree method and division method.

60

Exercise 1.1 | Q 11. b) | Page 11

Find the prime factorisation number by factor tree method and division method.

128

Exercise 1.1 | Q 11. c) | Page 11

Find the prime factorisation number by factor tree method and division method.

144

Exercise 1.1 | Q 11. d) | Page 11

Find the prime factorisation number by factor tree method and division method.

198

Exercise 1.1 | Q 11. e) | Page 11

Find the prime factorisation number by factor tree method and division method.

420

Exercise 1.1 | Q 11. f) | Page 11

Find the prime factorisation number by factor tree method and division method.

999

Exercise 1.1 | Q 12 | Page 11

If there are 143 math books to be arranged in equal numbers in all the stacks, then find the number of books in each stack and also the number of stacks.

#### Objective Type Questions

Exercise 1.1 | Q 13 | Page 12

The difference between two successive odd numbers is

• 1

• 2

• 3

• 0

Exercise 1.1 | Q 14 | Page 12

The only even prime number is

• 4

• 6

• 2

• 0

Exercise 1.1 | Q 15 | Page 12

Which of the following numbers is not a prime?

• 53

• 92

• 97

• 71

Exercise 1.1 | Q 16 | Page 12

The sum of the factors of 27 is

• 28

• 37

• 40

• 31

Exercise 1.1 | Q 17 | Page 12

The factors of a number are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80. What is the number?

• 80

• 100

• 128

• 160

Exercise 1.1 | Q 18 | Page 12

The prime factorisation of 60 is 2 × 2 × 3 × 5. Any other number which has the same prime factorisation as 60 is

• 30

• 120

• 90

• impossible

Exercise 1.1 | Q 19 | Page 12

If the number 6354*97 is divisible by 9, then the value of * is

• 2

• 4

• 6

• 7

Exercise 1.1 | Q 20 | Page 12

The number 87846 is divisible by

• 2 only

• 3 only

• 11 only

• all of these

Exercise 1.2 [Page 21]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 6th Mathematics Term 2 Answers Guide Chapter 1 NumbersExercise 1.2 [Page 21]

#### Fill in the blanks

Exercise 1.2 | Q 1. (i) | Page 21

The HCF of 45 and 75 is _________

Exercise 1.2 | Q 1. (ii) | Page 21

The HCF of two successive even numbers is __________

Exercise 1.2 | Q 1. (iii) | Page 21

If the LCM of 3 and 9 is 9, then their HCF is __________

Exercise 1.2 | Q 1. (iv) | Page 21

The LCM of 26, 39 and 52 is _________

Exercise 1.2 | Q 1. (v) | Page 21

The least number that should be added to 57 so that the sum is exactly divisible by 2, 3, 4 and 5 is __________

#### Say True or False

Exercise 1.2 | Q 2. (i) | Page 21

The numbers 57 and 69 are co-primes

• True

• False

Exercise 1.2 | Q 2. (ii) | Page 21

The HCF of 17 and 18 is 1

• True

• False

Exercise 1.2 | Q 2. (iii) | Page 21

The LCM of two successive numbers is the product of the numbers

• True

• False

Exercise 1.2 | Q 2. (iv) | Page 21

The LCM of two co-primes is the sum of the numbers

• True

• False

Exercise 1.2 | Q 2. (v) | Page 21

The HCF of two numbers is always a factor of their LCM

• True

• False

Exercise 1.2 | Q 3. (i) | Page 21

Find the HCF set of numbers using prime factorisation method.

18, 24

Exercise 1.2 | Q 3. (ii) | Page 21

Find the HCF set of numbers using prime factorisation method.

51, 85

Exercise 1.2 | Q 3. (iii) | Page 21

Find the HCF set of numbers using prime factorisation method.

61, 76

Exercise 1.2 | Q 3. (iv) | Page 21

Find the HCF set of numbers using prime factorisation method.

84, 120

Exercise 1.2 | Q 3. (v) | Page 21

Find the HCF set of numbers using prime factorisation method.

27, 45, 81

Exercise 1.2 | Q 3. (vi) | Page 21

Find the HCF set of numbers using prime factorisation method.

45, 55, 95

Exercise 1.2 | Q 4. (i) | Page 21

Find the LCM set of numbers using prime factorisation method.

6, 9

Exercise 1.2 | Q 4. (ii) | Page 21

Find the LCM set of numbers using prime factorisation method.

8, 12

Exercise 1.2 | Q 4. (iii) | Page 21

Find the LCM set of numbers using prime factorisation method.

10, 15

Exercise 1.2 | Q 4. (iv) | Page 21

Find the LCM set of numbers using prime factorisation method.

14, 42

Exercise 1.2 | Q 4. (v) | Page 21

Find the LCM set of numbers using prime factorisation method.

30, 40, 60

Exercise 1.2 | Q 4. (vi) | Page 21

Find the LCM set of numbers using prime factorisation method.

15, 25, 75

Exercise 1.2 | Q 5 | Page 21

Find the HCF and the LCM of the numbers 154, 198 and 286

Exercise 1.2 | Q 6 | Page 21

What is the greatest possible volume of a vessel that can be used to measure exactly the volume of milk in cans (in full capacity) of 80 litres, 100 litres and 120 litres?

Exercise 1.2 | Q 7 | Page 21

The traffic lights at three different road junctions change after every 40 seconds, 60 seconds and 72 seconds respectively. If they changed simultaneously together at 8 a.m at the junctions, at what time will they simultaneously change together again?

Exercise 1.2 | Q 8 | Page 21

The LCM of two numbers is 210 and their HCF is 14. How many such pairs are possible?

Exercise 1.2 | Q 9 | Page 21

The LCM of two numbers is 6 times their HCF. If the HCF is 12 and one of the numbers is 36, then find the other number

#### Objective Type Questions

Exercise 1.2 | Q 10 | Page 21

Which of the following pairs is co-prime?

• 51, 63

• 52, 91

• 71, 81

• 81, 99

Exercise 1.2 | Q 11 | Page 21

The greatest four-digit number which is exactly divisible by 8, 9 and 12 is

• 9999

• 9996

• 9696

• 9936

Exercise 1.2 | Q 12 | Page 21

The HCF of two numbers is 2 and their LCM is 154. If the difference between the numbers is 8, then the sum is

• 26

• 36

• 46

• 56

Exercise 1.2 | Q 13 | Page 21

Which of the following cannot be the HCF of two numbers whose LCM is 120?

• 60

• 40

• 80

• 30

Exercise 1.3 [Pages 22 - 23]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 6th Mathematics Term 2 Answers Guide Chapter 1 NumbersExercise 1.3 [Pages 22 - 23]

#### Miscellaneous Practice Problems

Exercise 1.3 | Q 1 | Page 22

Every even number greater than 2 can be expressed as the sum of two prime numbers. Verify this statement for every even number upto 16

Exercise 1.3 | Q 2 | Page 22

Is 173 a prime? Why?

Exercise 1.3 | Q 3 | Page 22

For which of the numbers, from n = 2 to 8, is 2n − 1 a prime?

Exercise 1.3 | Q 4. a) | Page 22

State true or false and explain your answer with reason for the following statement.

A number is divisible by 9, if it is divisible by 3

• True

• False

Exercise 1.3 | Q 4. b) | Page 22

State true or false and explain your answer with reason for the following statement.

A number is divisible by 6, if it is divisible by 12

• True

• False

Exercise 1.3 | Q 5. (i) | Page 22

Find A as required:

The greatest 2 digit number 9A is divisible by 2

Exercise 1.3 | Q 5. (ii) | Page 22

Find A as required:

The least number 567A is divisible by 3

Exercise 1.3 | Q 5. (iii) | Page 22

Find A as required:

The greatest 3 digit number 9A6 is divisible by 6

Exercise 1.3 | Q 5. (iv) | Page 22

Find A as required:

The number A08 is divisible by 4 and 9

Exercise 1.3 | Q 5. (v) | Page 22

Find A as required:

The number 225A85 is divisible by 11

Exercise 1.3 | Q 6 | Page 22

Numbers divisible by 4 and 6 are divisible by 24. Verify this statement and support your answer with an example

• True

• False

Exercise 1.3 | Q 7 | Page 22

The sum of any two successive odd numbers is always divisible by 4. Justify this statement with an example

• True

• False

Exercise 1.3 | Q 8 | Page 22

Find the length of the longest rope that can be used to measure exactly the ropes of length 1 m 20 cm, 3 m 60 cm and 4 m

#### Challenge Problems

Exercise 1.3 | Q 9 | Page 22

The sum of three prime numbers is 80. The difference of two of them is 4. Find the numbers

Exercise 1.3 | Q 10 | Page 22

Find the sum of all the prime numbers between 10 and 20 and check whether that sum is divisible by all the single digit numbers.

Exercise 1.3 | Q 11 | Page 22

Find the smallest number which is exactly divisible by all the numbers from 1 to 9

Exercise 1.3 | Q 12 | Page 22

The product of any three consecutive numbers is always divisible by 6. Justify this statement with an example

Exercise 1.3 | Q 13 | Page 22

Malarvizhi, Karthiga and Anjali are friends and natives of the same village. They work at different places. Malarvizhi comes to her home once in 5 days. Similarly, Karthiga and Anjali come to their homes once in 6 days and 10 days respectively. Assuming that they met each other on the 1st of October, when will all the three meet again?

Exercise 1.3 | Q 14 | Page 23

In an apartment consisting of 108 floors, two lifts A and B starting from the ground floor, stop at every 3rd and 5th floors respectively. On which floors, will both of them stop together?

Exercise 1.3 | Q 15 | Page 23

The product of 2 two digit numbers is 300 and their HCF is 5. What are the numbers?

Exercise 1.3 | Q 16 | Page 23

Find whether the number 564872 is divisible by 88. (use of the test of divisibility rule for 8 and 11 will help!)

Exercise 1.3 | Q 17 | Page 23

Wilson, Mathan and Guna can complete one round of a circular track in 10, 15 and 20 minutes respectively. If they start together at 7 a.m from the starting point, at what time will they meet together again at the starting point?

## Chapter 1: Numbers

Exercise 1.1Exercise 1.2Exercise 1.3 ## Tamil Nadu Board Samacheer Kalvi solutions for Class 6th Mathematics Term 2 Answers Guide chapter 1 - Numbers

Tamil Nadu Board Samacheer Kalvi solutions for Class 6th Mathematics Term 2 Answers Guide chapter 1 (Numbers) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Class 6th Mathematics Term 2 Answers Guide solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 6th Mathematics Term 2 Answers Guide chapter 1 Numbers are Divisibility by 10, Concept of Even and Odd Number, Factors and Multiples, Concept of Prime Numbers, Concept of Composite Number, Concept of Sieve of Eratosthenes, Concept of Twin Prime Numbers, Tests for Divisibility of Numbers, Divisibility by 2, Divisibility by 3, Divisibility by 5, Divisibility by 4, Divisibility by 6, Divisibility by 8, Divisibility by 9, Divisibility by 11, Prime Factorisation, Common Factor, Highest Common Factor, Common Multiples, Lowest Common Multiple, Relationship between the Numbers and their HCF and LCM.

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