**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