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Pra C Tice Ques Tions Factors and Multiples 2.9 TEST Your CONCEPTS Very Short Answer Type Questions Direction for questions from 1 to 5: Fill in the Direction for questions from 12 to 16: Fill in the blanks. blanks. 1. The number of factors of 24 is ______. 12. The number of common multiples of 6 and 15 is _____. 2. The greatest 2-digit multiple of 8 is _____. 13. The least common multiple of two co-primes is 3. The greatest common factor of 9 and 15 is _____. _____. 4. The number of prime factors of 48 is ______. 14. LCM (a, b) × HCF (a, b) = _____. 5. The greatest pair of twin primes of 2-digit 15. The largest 3-digit number divisible by 9 is _____. numbers is _____. 16. The smallest 4-digit number divisible by 11 is Direction for questions from 6 to 10: Select the _____. correct alternative from the given choices. Direction for questions from 17 to 22: Select the 6. Which of the following is a prime number? correct alternative from given choices. (a) 87 (b) 69 (c) 57 (d) 97 17. The LCM of a and b is 220. Which of the follow- 7. Which of the following is not a sphenic number? ing can be the HCF of a and b? (a) 30 (b) 42 (c) 60 (d) 70 (a) 33 (b) 15 (c) 20 (d) 12 8. Which of the following is a composite number? 18. Which of the following pairs of numbers have (a) 37 (b) 47 (c) 57 (d) 67 their LCM 144? 9. The HCF of which of the following pairs of com- (a) 18, 36 (b) 16, 96 posite numbers is different from that of the others? (c) 24, 48 (d) 9, 16 (Odd man out) 19. The HCF of the two numbers a and b is 12. Which (a) 12, 18 (b) 24, 30 of the following can be the LCM of a and b? (c) 18, 30 (d) 18, 45 (a) 44 (b) 65 (c) 76 (d) 96 10. Which of the following is the greatest measure that 20. Which of the following is divisible by 8, 15 and 6? can be used to measure the quantities 68 m, 102 m (a) 60 (b) 96 (c) 180 (d) 240 and 119 m? (a) 34 (b) 51 21. Which of the following is not divisible by 9? (c) 13 (d) 17 (a) 345672 (b) 278901 (c) 46938 (d) 96435 Direction for question 11: Match the Column A with the Column B. 22. Which of the following is divisible by 8? 11. (a) 7248882 (b) 836486 Column A Column B (c) 92304 (d) 726436 (a) Prime ( ) (p) Divisible by number only three Direction for question 23: Match the Column A prime numbers. with the Column B. (b) Sphenic ( ) (q) ‘2’ must be its 23. number factor. Column A Column B (a) 6, 8, 12 ( ) (p) 72 (c) Composite ( ) (r) It has at least number three factors. (b) 8, 12, 18 ( ) (q) 180 QUESTIONS PRACTICE (d) Even number ( ) (s) It has only two (c) 12, 18, 30 ( ) (r) 288 factors. (d) 18, 24, 32 ( ) (s) 24 M01_IIT_Class 6_C02.indd 9 3/29/2018 2:25:34 PM 2.10 Chapter 2 Short Answer Type Questions 24. List out all the common factors of the following 34. Find the LCM of 48, 60 and 280 by synthetic divi- pairs of numbers. sion method. (a) 120 and 160 (b) 52 and 32 35. The product of two numbers is 1680 and the LCM 25. List out all the 2-digit prime numbers which are of two numbers is 420. Find their HCF. greater than 50. 36. Find the greatest 3-digit number which is divisible 26. Express the following as the product of prime by 16, 18 and 24. numbers. 37. Find the smallest number greater than 2 which (a) 36 (b) 75 gives a remainder 2 when divided by 16, 18 and 24. 27. List out all the 2-digit twin primes. 38. Find the smallest number which when added by 6 28. Find the HCF of the following numbers by prime is exactly divisible by 9 and 33. factorization method. 39. Find the greatest 3-digit number which is a com- (a) 24, 60 (b) 48, 64, 80 mon multiple of 6, 15, and 21. 29. Find the HCF of 72, 140, 256 by division method. 40. Rishitha and Lohitha are twins. They play a game, in which they open a page of a text book printed in 30. Find the greatest number that divides 160, 264 English. From the first letter of the page, Rishitha leaving a remainder 4 in each case. strikes every 12th letter and Lohitha strikes every 31. Find the greatest number that divides 80 and 115 18th letter. If they strike the same letter 17 times leaving remainders 8 and 7 respectively. in the page, then find the minimum number of 32. On her birthday, Jyothsna received three differ- letters in the page selected. ent cakes of weight 3 kg, 2.6 kg and 2 kg from 41. Bhavagna celebrates her birthday every year. The her father, mother and sister respectively. She cut number of chocolates that she distributes every the three cakes into pieces of equal weights with- year is the greatest 3-digit common multiple of out any remainder. Find the minimum number of all the prime factors of the number representing pieces that she can get from the three cakes. that year. How many chocolates should Bhavagna 33. Find the LCM of 30, 75 and 120 by prime factor- distribute in the year 2016? ization method. CONCEPT APPLICATION 1. There are three empty drums which can hold 384 3. A father gave equal amount of money to his three litres, 576 litres and 288 litres of water. Each of daughters Simron, Cinderella and Sreya to purchase them is to be filled by using a measuring jar, a some items for his birthday party. Simron brought whole number of times. What is the largest pos- puffs which costs ` 18 each, Cinderella bought sible capacity of the measuring jar with which we cakes which costs ` 24 each and Sreya bought cool can fill all the three drums? drinks which costs ` 30 each. If they spent their (a) 96 litres (b) 24 litres money completely on these items, then find the (c) 72 litres (d) 36 litres minimum number of cakes that Cinderella bought. (a) 12 (b) 16 2. The dimensions of a hall are 6048 cm 2440 cm. × (c) 24 (d) 15 What is the minimum number of identical square shaped tiles that is required to furnish the hall? 4. Miss Sumitha has three drumsticks in her kitchen PRACTICE QUESTIONS PRACTICE (a) 2320 (b) 1061 which are 72 cm, 90 cm and 84 cm, respectively. She (c) 1240 (d) 2320 wanted to cut them into equal size of pieces. Find the minimum number of pieces that she can cut. M01_IIT_Class 6_C02.indd 10 3/29/2018 2:25:35 PM Factors and Multiples 2.11 (a) 41 (b) 58 the same coloured chairs and the number of chairs (c) 48 (d) 54 is equal in each row. Find the minimum number of rows of chairs in the auditorium. 5. There are 72 green colour, 144 red colour and 234 (a) 30 (b) 25 orange colour chairs in an auditorium. A boy want (c) 15 (d) 45 to put the chairs in rows such that each row is of ASSESSMENT TEST 1. List out all the common factors of 64 and 96. skips 20 times in a minute. Both of them start skip- ping at 4.50 p.m. and continue till 5 p.m. without 2. Write all the common prime factors of 720 and any interruption. How many times do they skip 140. the rope simultaneously after 4.50 p.m.? 3. Find the HCF of 126 and 144 by prime factoriza- 10. Write the first three multiples of 48. tion method. 11. Write three factors of 48. 4. Find the HCF of 84 and 112 by division method. 12. Which of the following pairs are co-prime? 5. Find the least common multiple of 8, 15 and 20 by prime factorization method. 2, 3; 8, 9; 21, 22 6. Find the least common multiple of 24, 40 and 60 13. Which of the following numbers are divisible by 5, by synthetic division. 55, 556, 50058, 85501? 7. The LCM of two numbers is 112 and their HCF 14. Is 199 a prime number? is 2. If one of the numbers is 14, then find the 15. Two bags of sugar contain 26 and 39 kg of sugar, other number. respectively. What is the greatest weight that can 8. A number P is divisible by 5, 4, 8 and 9. If p is a be used to measure the weight in each bag an exact 3-digit number, then find all the possible values number of times? How many times will it take for P. to weigh all the sugar in the two bags using this weight? 9. Aakruthi and Prakruthi are playing skipping-rope. Aakruthi skips 30 times in a minute and Prakruthi CROSSWORD 1 2 3 4 5 6 7 8 PRACTICE QUESTIONS PRACTICE 9 10 11 M01_IIT_Class 6_C02.indd 11 3/29/2018 2:25:35 PM 2.12 Chapter 2 Across Down 4. The natural numbers having more than two factors 1. The name of divisor when the remainder is 0 8. The units digit of an odd number which is divis- 2.
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