ML Aggarwal CBSE Solutions Class 6 Math Third Chapter Playing with Numbers Exercise 3.1

ML Aggarwal CBSE Solutions Class 6 Math Chapter Playing with Numbers Exercise 3.1

(1) Fill in the blanks:

(i) A number having exactly two factors is called a _____

Ans. Prime number.

(ii) a number having more than two factors is called a  _____

Ans. composite number

(iii) 1 is neither _____ or ____

Ans. prime, composite

(iv) The smallest primer number is  ______

Ans. 2

(v) The smallest odd prime number is ______

Ans. 3

(vi) The smallest composite number is _______

Ans. 4

(vii) The smallest odd composite number is _____

Ans. 9

(viii) All prime numbers (except 2) are ______

Ans. Odd numbers

(2) State whether the following statement is True or False

(i) False

(ii) False

(iii) False

(iv) True

(v) True

(vi) False

(vii) False

(viii) True

(3) Write all the factors of the following natural numbers:

(i) 68 – 1, 2, 4, 17, 34, 68

(ii) 27 – 1, 3, 9, 27

(iii) 210 – 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

(4) Write first six multiples of the following natural numbers:

(i) 3 – 3 x 1 = 3; 3 x 2 = 6; 3 x 3 = 9; 3 x 4 = 12; 3 x 5 = 15.

(ii) 5 – 5, 10, 15, 20, 25, 30

(iii) 12 – 12. 24, 36, 48, 60, 72

(5) Math the items in column 1 with the items in column 2:

Solution:

Column 1 Column 2
(i) 15 (b) Factor of 30
(ii) 36 (e) Multiple of 9
(iii) 16 (a) Multiple of 8
(iv) 20 (f) Factor of 20
(v) 25 (d) Factor of 50
(vi) 210 (c) Multiple of 70

(6) Find the common factors of:

(i) 20 and 28

Solution: 20 = 1, 2, 4, 5, 10, 20

28 = 1, 2, 4, 7, 14, 28

Common factors are = 1, 2, 4

(ii) 35 and 50

Solution: 35 – 1, 5, 7, 35

50 – 1, 2, 5, 10, 25, 50

Common factors are – 1, 5

(iii) 56 and 120

Solution: 56 – 1, 2, 4, 7, 8, 14, 28, 56

120 – 1, 2, 3. 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60,120

Common factors are – 1, 2, 4, 8

(7) Find the common factors of:

(i) 4, 8, 12

4 – 1, 2, 4

8 – 1, 2, 4, 8

12 – 1, 2, 3, 4, 6, 12

Common factors are – 1, 2, 4

(ii) 10, 30 and 35

10 – 1, 2, 5. 10

30 – 1, 2, 3, 5, 6, 10, 15, 30

35 – 1, 5, 7, 35

Common factors are – 1 & 5

(8) Write all natural numbers less than 100 which are common multiples of 3 and 4.

Solution: Multiple of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99

Multiple of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100

Common multiples of 3 and 4 = 12, 24, 36, 48, 60, 72, 84, 96

(9) (i) Write the odd numbers between 36 and 53.

Solution: The  numbers are – 37, 39, 41, 43, 45, 47, 49, 51

(ii) Write the even numbers between 232 and 251.

Solution: The even numbers between 232 and 251 are – 234, 236, 238, 240, 242, 244, 246, 248, 250

(10) (i) Write four consecutive odd numbers succeeding 79.

Solution: Four consecutive odd numbers succeeding 79 are – 81, 83, 85, 87

(ii) Write three consecutive even numbers preceding 124

Solution: Three consecutive even numbers preceding 124 are: 118, 120, 122

(11) What is the greatest prime number between 1 and 15?

Solution: The greatest prime number between 1 and 15 is 13

(12) Which of the following numbers are prime?

(i) 29

(ii) 57

(iii) 43

(iv) 61

Solution: 29, 57 and 43 are prime numbers as they are only two factor one and itself.

(13) Which of the following pairs of numbers are co-prime?

(i) 12 and 35 (ii) 15 and 37 (iii) 27 and 32 (iv) 17 and 85 (v) 515 and 516 (vi) 215 and 415

Solution: (i) The factor of 12 are – 1, 2, 3, 4, 6, 12

The factor of 35 are – 1, 5, 7, 35

We note that 1 is the only common factor of 12 and 35

Therefore, 12 and 35 are co primes.

(ii) 15 and 37

Factor of 15 are – 1, 3, 5, 15

Factor of 37 are – 1, 37

There are no common factor between 15 and 37 except 1, so 15 and 37 are co primes.

(iii) 27 and 32

Factor of 27 – 1, 3, 9, 27

Factor of 32 – 1, 2, 4, 8, 16, 32

There are no common factor between 27 and 32 except 1 so,

27, 32 is a common factor.

(iv) 17 and 85

Factors of 17 – 1, 17

Factor of 85 – 1, 5, 17. 85

There are common factors of 17 and 85 except 1 is 17

So 17 and 85 are not co-primes.

(v) 515 and 516

The factors of 515 = 1, 5, 103, 515

The factors of 516 = 1, 2, 258, 516

There are no common factors between 515 and 516 except 1

So, 515 and 516 are co-prime.

(vi) 215 and 415

Solution: Both are odd numbers. And both numbers last digit is 5 so both numbers divisible by 5.

Therefore, 215 and 415 are co prime.

(14) Express each of the following numbers as the sum of two odd primes.

Solution: (i) 24 = 11 + 13

(ii) 36 = 23 + 13

(iii) 84 = 51 + 33

(iv) 98 = 65 + 33

(15) Express each of the following numbers as the sum of twin primes.

Solution: (i) 24 = 11 + 13

(ii) 36 = 17 + 19

(iii) 84 = 41 + 43

(iv) 120 = 59 + 61

(16) Express each of the following numbers as the sum of three odd primes:

(i) 21 = 3 + 7 + 11

(ii) 35 = 5 + 11 + 19

(iii) 49 = 7 + 11 + 31

(iv) 63 = 7 + 13 + 43

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