Page 301 - Ganit Kaushal

5. (a) Not co-prime (b) Co-prime 9. (a) 3 7 3 63 (b) 7 7 7 343
6. (a) Divisible (b) Not divisible 3 3 3 27 2 11 3 66
[Hint:  These are divisible by 8 and 5. See Ex. 18] 5 2 19 190 2 2 11 44
7. 5600, 6000 and 77622160. 45 42 171 28 154 231

8. 9, 4 and 1 receptively. 10. 4, 9, 49 (factors of 4 = 1, 2, 4; factors of 9 = 1, 3, 9;
9. 7 5 3 105 factors of 49 = 1, 7, 49.);
2 5 2 20 All these are squares of prime numbers.
2 5 3 30 11. 17, 71, 35, 53
28 125 18 12. (a) 729 = 3 × 3 × 3 × 3 × 3 × 3
10. 9999 (b) 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
(c) 1331 = 11 × 11 × 11
9 1111 (d) 1000 = 2 × 2 × 2 × 5 × 5 × 5
13. (i) (a) 2 (b) 8 (ii) (a) 0 (b) 9
3 3 11 101 Assertion Reason Type Questions
11. (a) False [ 12 is divisible by 4 but not by 8] 1. (a) 2. (b) 3. (d) 4. (a)
(b) True [ 4 is a factor of 8] 5. (a) 6. (d) 7. (c) 8. (d)
(c) True [by Property-3 of divisibility] 9. (a)
(d) False [ 10 + 5 = 15 is divisible by 3 but none of Case Study Based Questions
10 and 5.] 1. (a) 19 (b) 10 (c) 3 (d) 12
Miscellaneous Exercise 5.4 (e) 17
1. (b) 2. (d) 3. (d) 4. (a) Chapter Test
5. (a) 6. (a) I. 1. (c) 2. (b) 3. (d) 4. (b)
7. (a) 1 (b) 2 (c) 6, 28 (Answer may vary) 5. (d) 6. (b) 7. (c)
(d) 3, 5, 7 (e) 1 (f) 2 (g) co-prime II. 1. factor/multiple 2. 1, number itself
(h) 0 (i) perfect (j) composite 3. 2 4. 1 5. twin prime
(k) prime (l) multiple (m) HCF 6. 9 7. 1 8. 0
8. (a) True (b) True (c) True (d) True 9. factors/divisors
(e) True III. 1. False [ 9 is an odd number but not prime]
(f) False; 2 and 7 both are prime, but their sum is an 2. False [ 1 is a square number, but not composite]
odd number. 3. False [ It is a sum of all its proper factors or twice

(g) False; 3 and 5 both are prime numbers, but their the sum of all its factors]
sum is a composite number. 4. False [ 2 is the smallest prime number]
(h) False; 2 and 5 both are prime numbers, but their 5. True
sum is a prime number. 6. False [ Prime factorisation of a number is unique]
(i) False; 13 is an odd number and 13 = 2 + 11, which
is sum of two prime numbers. 7. True

(j) False; 8 and 15 are co-prime numbers, but neither 8. False [ 5 + 7 = 12 is divisible by 2, but neither 5
nor 7 is divisible by 2.]
8 nor 15 is prime.
(k) True IV. 1. (b) 613440
3, 7, 30, 70, 37, 73, 307, 370, 703, 730.
2.
(l) False; 20 is divisible by 2 and 4 both. But 20 is not
divisible by 8. 3. (a) 2 × 2 × 2 × 3 × 7
(m) False; 12 is divisible by 3 and 6 both, but 12 is not (b) 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
divisible by 18. 4. 14, 28, 42, 56, …... at first 15 multiples of 14.
(n) True 5. (a) Æ (ii) (b) Æ (iv) (c) Æ (i) (d) Æ (vi)
(o) True (e) Æ (v)

Answers 299