{"id":3600,"date":"2022-05-12T09:46:27","date_gmt":"2022-05-12T09:46:27","guid":{"rendered":"https:\/\/hbsesolutions.com\/?p=3600"},"modified":"2022-05-13T05:50:54","modified_gmt":"2022-05-13T05:50:54","slug":"hbse-6th-class-maths-solutions-chapter-3-ex-3-5","status":"publish","type":"post","link":"https:\/\/hbsesolutions.com\/hbse-6th-class-maths-solutions-chapter-3-ex-3-5\/","title":{"rendered":"HBSE 6th Class Maths Solutions Chapter 3 Playing With Numbers Ex 3.5"},"content":{"rendered":"

Haryana State Board HBSE 6th Class Maths Solutions<\/a> Chapter 3 Playing With Numbers Ex 3.5 Textbook Exercise Questions and Answers.<\/p>\n

Haryana Board 6th Class Maths Solutions Chapter 3 Playing With Numbers Exercise 3.5<\/h2>\n

Question 1.
\nWhich of the following state\u00acments are true ?
\n(a) If a number is divisible by 3, it must be divisible by 9.
\n(b) If a num ber is divisible is 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 that numbers divisible by 4 must also be divisible by 8.
\n(g) All that numbers divisible by 8 must also be divisible by 4.
\n(h) The sum of two consecutive odd numbers is divisible by 4.
\n(i) If a number exactly divides two numbers separately, it must exactly divide their sum.
\n(j) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.
\nSolution:
\n(a) F, (b) T, (c) T, (d) T, (e) F, (\/) F, (g) T, (h) T, (i) T, (\/) F.<\/p>\n

Question 2.
\nHere are two different factor trees for 60. Write the missing numbers.
\n\"HBSE
\nSolution:
\n\"HBSE<\/p>\n

\"HBSE<\/p>\n

Question 3.
\nWhich factors are not included in the prime factorisation of a composite number ?
\nSolution:
\nLet us consider any composite number say 12.
\n12 = 1 x 12
\n= 2 x 6
\n= 3 x 4
\nand
\n\"HBSE
\n\u2234 Factors of 12 are : 1, 2, 3, 4, 6, 12.
\nPrime factorisation of 12 = 2 x 2 x 3
\nWe clearly see that composite factors 4, 6, 12 are not included in the prime factorisation of a composite number.
\nHence, composite factors are not included in the prime factorisation of a composite number.<\/p>\n

Question 4.
\nWrite the greatest four-digit number and express it into the form of prime factorisation.
\nSolution:
\nGreatest 4-digit number is 9999.
\n\"HBSE
\n\u2234 Prime factorisation of 9999
\n= 3 x 3 x 11 x 101<\/p>\n

\"HBSE<\/p>\n

Question 5.
\nWrite the smallest five-digit number and express it into the form of prime factorisation.
\nSolution:
\nSmallest 5-digit number is 10000
\n\"HBSE
\n\u2234 Prime factorisation of 10000
\n= 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5.<\/p>\n

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.
\nSolution:
\n\"HBSE
\n\u2234 Prime factors of 1729 are 7, 13, 19
\nDifference between two consecutive prime factors is 6.<\/p>\n

Question 7.
\nThe product of three consecutive numbers is always divisible by 6. Explain this statement with the help of some examples.
\nSolution:
\n(i) Let us take three consecutive numbers 5, 6, 7.
\nTheir product = 5 x 6 x 7 = 210 which is divisible by 6.
\n(ii) Let us take three consecutive numbers 9, 10, 11.
\nTheir product = 9 x 10 x 11 = 990 which is divisible by 6.
\n(iii) Let us take three consecutive numbers 23, 24, 25.
\nTheir product = 23 x 24 x 25 = 13800 which is divisible by 6.
\n(iv) Let us take three consecutive numbers 2, 3, 4.
\nTheir product = 2 x 3 x 4 = 24 which indivisible by 6.<\/p>\n

Question 8.
\nIn which of the following expressions, prime factorisation has been done :
\n(a) 24 = 2 x 3 x 4
\n(b) 56 = 1 x 7 x 2 x 2 x 2
\n(c) 70 = 2 x 5 x 7
\n(d) 54 = 2 x 3 x 9.
\nSolution:
\n(c) 70 = 2 x 5 x 7.
\nIn this expression prime factorisation has been done.
\n(b) 56 = 1 x 7 x 2 x 2 x 2 In this expression prime factorisation has been done.<\/p>\n

\"HBSE<\/p>\n

Question 9.
\nWrite the prime factorisation of 15470.
\n\"HBSE
\n\u2234 Prime factorisation of 15470
\n= 2 x 5 x 7 x 13 x 17.<\/p>\n

Question 10.
\nDetermine if 25110 is divisible by 45.
\nSolution:
\n\u2235 The unit\u2019s digit of 25110 is 0,
\n\u2234 25110 is divisible by 5.
\nSum of the digits = 2 + 5+ l + l + 0 = 9 which is divisible by 9.
\n\u2234 25110 is divisible by 9.
\nNow, 5 and 9 are co-prime numbers.
\n\u2234 25110 is divisible by their product 5 x 9 = 45.<\/p>\n

Question 11.
\n18 is divisible by both 2 and 3. It is also divisible by 2 x 3 = 6. Similarly, a number is divisible by both 4 and 6. Can we say that the number must also be divisible by 4 x 6 = 24 ? If not, give an example to justify your answer.
\nSolution:
\nNo, because 4 and 6 are not co-primes.
\ne.g. (i) 36 is divisible by both 4 and 6. But it is not divisible by 24.
\n(ii) 12 is divisible by both 4 and 6 but 12 is not divisible by 24.<\/p>\n

\"HBSE<\/p>\n

Question 12.
\nI am the smallest number having four different prime factors. Can you find me ?
\nSolution:
\nThe smallest four different prime factors are 2, 3, 5, 7.
\nHence, the smallest number, having four different prime factors = 2 x 3 x 5 x 7 = 210.<\/p>\n","protected":false},"excerpt":{"rendered":"

Haryana State Board HBSE 6th Class Maths Solutions Chapter 3 Playing With Numbers Ex 3.5 Textbook Exercise Questions and Answers. Haryana Board 6th Class Maths Solutions Chapter 3 Playing With Numbers Exercise 3.5 Question 1. Which of the following state\u00acments are true ? (a) If a number is divisible by 3, it must be divisible …<\/p>\n

HBSE 6th Class Maths Solutions Chapter 3 Playing With Numbers Ex 3.5<\/span> Read More »<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","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":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":"","footnotes":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/hbsesolutions.com\/wp-json\/wp\/v2\/posts\/3600"}],"collection":[{"href":"https:\/\/hbsesolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hbsesolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hbsesolutions.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/hbsesolutions.com\/wp-json\/wp\/v2\/comments?post=3600"}],"version-history":[{"count":1,"href":"https:\/\/hbsesolutions.com\/wp-json\/wp\/v2\/posts\/3600\/revisions"}],"predecessor-version":[{"id":3643,"href":"https:\/\/hbsesolutions.com\/wp-json\/wp\/v2\/posts\/3600\/revisions\/3643"}],"wp:attachment":[{"href":"https:\/\/hbsesolutions.com\/wp-json\/wp\/v2\/media?parent=3600"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hbsesolutions.com\/wp-json\/wp\/v2\/categories?post=3600"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hbsesolutions.com\/wp-json\/wp\/v2\/tags?post=3600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}