NCERT Solutions for Class 6 Maths<\/a> Chapter 3 Playing With Numbers Ex 3.5 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\nNCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Exercise 3.5<\/h2>\n Question 1. \nWhich of the following statements are true: \n(a) If a number is divisible by 3, it must be divisible by 9. \n(b) If a number is divisible by 9, it must be divisible by 3. \n(c) A number is divisible by 18, if it is divisible by both 3 and 6. \n(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90. \n(e) If two numbers are co-primes, at least one of them must be prime. \n(f) All numbers which are divisible by 4 must also be divisible by 8. \n(g) All numbers which are divisible by 8 must also be divisible by 4. \n(h) If a number exactly divides two numbers separately, it must exactly divide their sum. \n(i) If a number is exactly divides the sum of two numbers, it must exactly divide the two numbers separately. \nAnswer: \nStatements (b), (d), (g) and (h) are true.<\/p>\n
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Question 2. \nHere are two different factor trees for 60. Write the missing numbers. \n \nAnswer: \n \nSince, 6 = 2 \u00d7 3 \nand 10 = 5 \u00d7 2 \n \nSince, 60 = 30 \u00d7 2 \n30= 10 \u00d7 3 \n10 = 5 \u00d7 2<\/p>\n
Question 3. \nWhich factors are not included in the prime factorisation of a composite number? \nAnswer: \n1 and the number it self are not included in the prime factorisation of a composite number.<\/p>\n
Question 4. \nWrite the greatest 4-digit number and express it in terms of its prime factors. \nAnswer: \nThe greatest 4-digit number = 9999 \n \nThe prime factors of 9999 are 3 \u00d7 3 \u00d7 11 \u00d7 101.<\/p>\n
Question 5. \nWrite the smallest 5-digit number and express it in the form of its prime factors. \nAnswer: \nThe smallest five digit number is 10000. \n \nThe prime factors of 10000 are 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 5 \u00d7 5 \u00d7 5 \u00d7 5.<\/p>\n
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Question 6. \nFind all the prime factors of 1729 and arrange them in ascending order. Now state the relation, if any, between, two consecutive prime factors. \nAnswer: \nPrime factors of 1729 are 7 \u00d7 13 \u00d7 19. \n \nThe difference of two consecutive prime factors is 6.<\/p>\n
Question 7. \nThe product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples. \nAnswer: \nAmong the three consecutive numbers, there must be one even number and one multiple of 3. Thus, the product must be multiple of 6. \nExample: (i) 2 \u00d7 3 \u00d7 4 = 24 \n(ii) 4 \u00d7 5 \u00d7 6 = 120<\/p>\n
Question 8. \nThe sum of two consecutive odd numbers is divisible by 4. Verify this statement with the help of some examples. \nAnswer: \n3 + 5 = 8 and 8 is divisible by 4. \n5 + 7 = 12 and 12 is divisible by 4. \n7 + 9 = 16 and 16 is divisible by 4. \n9 + 11 = 20 and 20 is divisible by 4.<\/p>\n
Question 9. \nIn which of the following expressions, prime factorisation has been done? \n(a) 24 = 2 \u00d7 3 \u00d7 4 \n(b) 56 = 7 \u00d7 2 \u00d7 2 \u00d7 2 \n(c) 70 = 2 \u00d7 5 \u00d7 7 \n(d) 54 = 2 \u00d7 3 \u00d7 9 \nAnswer: \nIn expressions (b) and (c), prime factorisation has been done.<\/p>\n
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Question 10. \nDetermine if 25110 is divisible by 45. [Hint: 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9. \nAnswer: \nThe prime factorization of 45 = 5 \u00d7 9 \n25110 is divisible by 5 as \u20180\u2019 is at its unit place. \n25110 is divisible by 9 as sum of digits is divisible by 9. \nTherefore, the number must be divisible by 5 \u00d7 9 = 45<\/p>\n
Question 11. \n18 is divisible by both 2 and 3. It is also divisible by 2 \u00d7 3 = 6. Similarly, a number is divisible by 4 and 6. Can we say that the number must be divisible by 4 \u00d7 6 = 24? If not, give an example to justify your answer. \nAnswer: \nNo, Number 12 is divisible by both 6 and 4 but 12 is not divisible by 24.<\/p>\n
Question 12. \nI am the smallest number, having four different prime factors. Can you find me? \nAnswer: \nThe smallest four prime numbers are 2, 3, 5 and 7. \nHence, the required number is 2 \u00d7 3 \u00d7 5 \u00d7 7 = 210<\/p>\n","protected":false},"excerpt":{"rendered":"
These\u00a0NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.5 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Exercise 3.5 Question 1. Which of the following statements are true: (a) If a number is divisible by 3, it …<\/p>\n
NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.5<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[10],"tags":[],"yoast_head":"\nNCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.5 - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n