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