{"id":16780,"date":"2019-12-31T11:55:14","date_gmt":"2019-12-31T06:25:14","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=16780"},"modified":"2021-07-02T15:33:08","modified_gmt":"2021-07-02T10:03:08","slug":"kseeb-solutions-for-class-6-maths-chapter-3-ex-3-5","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/kseeb-solutions-for-class-6-maths-chapter-3-ex-3-5\/","title":{"rendered":"KSEEB Solutions for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.5"},"content":{"rendered":"

Students can Download Chapter 3 Playing with Numbers Ex 3.5 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 6 Maths<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka State Syllabus Class 6 Maths Chapter 3 Playing with Numbers Ex 3.5<\/h2>\n

Question 1.
\nWhich of the following statements are true?
\na) If a number is divisible by 3, it must be divisible by 9.
\nb) If a number is divisible by 9, it must be divisible by 3.
\nc) A number is divisible by 18, if it is divisible by both 3 and 6.
\nd) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
\ne) If two numbers are co-primes, at least one of them must be prime.
\nf) All numbers which are divisible by 4 must also be divisible by 8.
\ng) All numbers which are divisible by 8 must also be divisible by 4.
\nh) If a number exactly divides two numbers separately, it must exactly divide their sum.
\ni) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.
\nSolution:
\n(a) False
\n6 is divisible by 3, but not by 9.<\/p>\n

(b) True, as 9 = 3 \u00d7 3
\nTherefore, if a number is divisible by 9, then it will also be divisible by 3.<\/p>\n

(c) False
\n30 is divisible by 3 and 6 both, but it is not divisible by 18.<\/p>\n

(d) True, as 9 \u00d7 10 = 90
\nTherefore, if a number is divisible by 9 and 10 both, then it will also be divisible by 90.<\/p>\n

(e) False
\n15 and 32 are co-primes and also composite.<\/p>\n

\"KSEEB<\/p>\n

(f) False
\n12 is divisible by 4, but not by 8.<\/p>\n

(g) True, as 8 = 2 \u00d7 4
\nTherefore, if a number is divisible by 8, then it will also be divisible by 2 and 4.<\/p>\n

(h) True
\n2 divides 4 and 8 as well as 12. (4 + 8 = 12)<\/p>\n

(i) False
\n2 divides 12, but does not divide 7 and 5.<\/p>\n

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

Question 3.
\nWhich factors are not included in the prime factorisation of a composite number ?
\nSolution:
\n1 and the number itself.<\/p>\n

\"KSEEB<\/p>\n

Question 4.
\nWrite the greatest 4-digit number and express it in terms of its prime factors.
\nSolution:
\nGreatest four-digit number = 9999
\n9999 = 3 \u00d7 3 \u00d7 11 \u00d7 101
\n\"KSEEB<\/p>\n

Question 5.
\nWrite the smallest 5-digit number and express it in the form of its prime factors.
\nSolution:
\n\"KSEEB
\n10,000
\n= 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 5 \u00d7 5 \u00d7 5 \u00d7 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:
\n1729 = 7 \u00d7 13 \u00d7 19
\n13 – 7 = 6, 19 – 13 = 6
\n\"KSEEB
\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.
\nSolution:
\n2 \u00d7 3 \u00d7 4 = 24, which is divisible by 6
\n9 \u00d7 10 \u00d7 11 = 990, which is divisible by 6
\n20 \u00d7 21 \u00d7 22 = 9240, which is divisible by 6<\/p>\n

Question 8.
\nThe sum of two consecutive odd numbers is divisible by 4. Verily this statement with the help of some examples.
\nSolution:
\n3 + 5 = 8, which is divisible by 4
\n15 + 17 = 32, which is divisible by 4
\n19 + 21 = 40, which 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
\nSolution:
\na) 24 = 2 \u00d7 3 \u00d7 4
\nSince 4 is composite, prime factorisation has not been done.<\/p>\n

(b) 56 = 7 \u00d7 2 \u00d7 2 \u00d7 2
\nSince ail the factors are prime, prime factorisation has been done.<\/p>\n

(c) 70 = 2 \u00d7 5 \u00d7 7
\nSince all the factors are prime, prime factorisation has been done.<\/p>\n

(d) 54 = 2 \u00d7 3 \u00d7 9
\nSince 9 is composite, prime factorisation has not been done.<\/p>\n

Question 10.
\nDetermine if 25110 is divisible by 45.
\n|Hint: 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9|.
\nSolution:
\n45 = 5 \u00d7 9
\nFactors of 5 = 1, 5
\nFactors of 9 = 1, 3, 9
\nTherefore, 5 and 9 are co-prime numbers. Since the last digit of 25110 is 0, it is divisible by 5.
\nSum of the digits of 25110 = 2 + 5 + 1 + 1 + 0 = 9
\nAs the sum of the digits of 25110 is divisible by 9. therefore, 25110 is divisible by 9.
\nSince the number is divisible by 5 and 9 both, it is divisible by 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 both 4 and 6. Can we say that the number must also be divisible by 4 \u00d7 6 = 24? If not, give an example to justify your answer.
\nSolution:
\nNo. It is not necessary because 12 and 36 are divisible by 4 and 6 both, but are not divisible by 24.<\/p>\n

\"KSEEB<\/p>\n

Question 12.
\nI am the smallest number, having four different prime factors. Can you find me?
\nSolution:
\nSince it is the smallest number of such type, it will be the product of 4 smallest prime numbers.
\n2 \u00d7 3 \u00d7 5 \u00d7 7 = 210<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Chapter 3 Playing with Numbers Ex 3.5 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 6 Maths helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka State Syllabus Class 6 Maths Chapter 3 Playing with Numbers Ex 3.5 Question 1. Which of …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[83],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/16780"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=16780"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/16780\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=16780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=16780"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=16780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}