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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________
(b) 3.
12 Divisible By
8 16 Number Digit Total
24 36 60 2 3 4 5 6 7 8 9 10 11
32 40 48 27 2 + 7 = 9 No Yes No No No No No Yes No No
72
56 96 84 74 7 + 4 = 11 Yes No No No No No No No No No
64
80 108 132 1 + 3 + 2 = 6 Yes Yes Yes No Yes No No No No Yes
165 1 + 6 + 5 = 12 No Yes No Yes No No No No No Yes
Multiples of 8 Multiples of 12
184 1 + 8 + 4 = 13 Yes No Yes No No No Yes No No No
12. (7, 8) (Answers may vary) 207 2 + 0 + 7 = 9 No Yes No No No No No Yes No No
Think and Answer
1. 2 (Even) 2. 4 (Even) 280 2 + 8 + 0 = 10 Yes No Yes Yes No Yes Yes No Yes No
3. 15; These are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. 131 1 + 3 + 1 = 5 No No No No No No No No No No
4. No, e.g., 6 has more number of factors than 9. 506 5 + 0 + 6 = 11 Yes No No No No No No No No Yes
Practice Time 5C 283 2 + 8 + 3 = 13 No No No No No No No No No No
1. (a) F (b) T (c) T (d) F
(e) F (f) T (g) F (h) F 147 1 + 4 + 7 = 12 No Yes No No No Yes No No No No
2. 10; These are 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 385 3 + 8 + 5 = 16 No No No Yes No Yes No No No Yes
3. (a) Yes (b) Yes (c) No (d) Yes 250 2 + 5 + 0 = 7 Yes No No Yes No No No No Yes No
4. (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).
5. (3, 7), (3, 11), (3, 19) (Answers may vary) 477 4 + 7 + 7 = 18 No Yes No No No No No Yes No No
6. (a) Yes, 3 + 3 + 7 = 13, 5 + 7 + 11 = 23 (Answer may vary) 824 8 + 2 + 4 = 14 Yes No Yes No No No Yes No No No
(b) No. 753 7 + 5 + 3 = 15 No Yes No No No No No No No No
7. 101, 103, 107, 109, 113, 127, 131, 137, 139,149,151,157, 163, 167, 173,
179, 181, 191, 193, 197, 199. 1325 1 + 3 + 2 + 5 = 11 No No No Yes No No No No No No
8. One – 523 4. (c) 46938
Think and Answer 5. (a) Yes (b) No (c) No (d) Yes (e) Yes (f) No
210 = 2 × 3 × 5 × 7 6. (a) Yes (b) No (c) Yes (d) Yes
Practice Time 5D
7. (a) 48 = 5 + 43 (b) 64 = 11 + 53
1. (a) 72 (b) 450 (c) 96 = 7 + 89 [Answers may vary]
8. (a) 27 = 3 + 5 + 19 (b) 41 = 3 + 7 + 31
2 36 2 225 (c) 63 = 3 + 7 + 53 [Answers may vary]
9. (a) 36 = 17 + 19 (b) 84 = 41 + 43
18 2 15 15
10. 25 = 2 + 23; 26 = 3 + 23; 31 = 7 + 11 + 13 [Answers may vary]
9 2 3 5 3 5 11.
3 3
(c) 50 (d) 81
2 25 9 9
5 5 3 3 3 3 12. (a) – (iv) (b) – (i) (c) – (ii) (d) – (iii)
13. (a) Prime number (b) Composite number
2. (a) 105 = 3 × 5 × 7 (b) 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
(c) 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 (c) Composite number (d) Composite number
(d) 729 = 3 × 3 × 3 × 3 × 3 × 3 14. 175662 16. (a) 928389 (b) 819489
3. (a) 3 × 47 (b) 2 × 2 × 2 × 5 × 5 × 5 Quick Check
(c) 11 × 11 × 11 (d) 5 × 5 × 5 × 5
4. (a) 30 = 2 × 3 × 5 (b) 2310 = 2 × 3 × 5 × 7 × 11 1. (a) 8 (b) 24 2. (a) 1 (b) 2 (c) 1
5. (a) Yes (b) No (c) No (d) No Think and Answer
6. Perfect number: 496
Abundant number: 18 1152
Deficient number:11 [Answers may vary] Quick Check
7. (1184, 1210) [Answers may vary] 1. 5 2. 150
Think and Answer Practice Time 5F
1324
Think and Answer 1. (a) 2 (b) 2 (c) 2
(3, 10) is a pair of co-prime 2. (a) 4 (b) 12 (c) 1 (d) 79
Practice Time 5E 3. (a) 84 (b) 90 (c) 336
1. (a) No (b) Yes (c) No (d) Yes 4. (a) 240 (b) 180 (c) 12626
2. (a) No (b) No (c) Yes (d) Yes 5. 9:12 a.m. 6. 31 cm 7. 158 8. 1540 9. 12 minutes.
317 Answers

