{"id":8308,"date":"2024-01-30T15:52:39","date_gmt":"2024-01-30T10:22:39","guid":{"rendered":"https:\/\/tsboardsolutions.in\/?p=8308"},"modified":"2024-02-03T09:33:10","modified_gmt":"2024-02-03T04:03:10","slug":"ts-6th-class-maths-solutions-chapter-3-ex-3-4","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.in\/ts-6th-class-maths-solutions-chapter-3-ex-3-4\/","title":{"rendered":"TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.4"},"content":{"rendered":"

Students can practice TS 6th Class Maths Solutions<\/a> Chapter 3 Playing with Numbers Ex 3.4 to get the best methods of solving problems.<\/p>\n

TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Exercise 3.4<\/h2>\n

Question 1.
\nFind the HCF of the following numbers by prime factorisation and continued division method.
\n(i) 18, 27, 36
\nAnswer:
\nThe given numbers are
\n18, 27, 36<\/p>\n

Prime factorisation method:
\n\"TS
\nThe common factor of 18, 27 and 36 is 3 \u00d7 3 = 9
\nHence, HCF of 18, 27 and 36 is 9.<\/p>\n

Continued division method :
\nThe given numbers are 18, 27 and 36.
\nLet us find the HCF of 18 and 27.
\n\"TS
\n\u2234 HCF of 18 and 27 is 9.
\nLet us find the HCF of third number and the HCF of first.two numbers.
\nLet us find the HCF of 36 and 9.
\n\"TS
\nHCF of 18, 27 and 36 is 9.<\/p>\n

\"TS<\/p>\n

(ii) 106, 159, 265
\nAnswer:
\nThe given numbers are 106, 159 and 265.<\/p>\n

Prime factorisation method:
\n\"TS
\n\u2234 The common factor of 106, 159 and 265 is 53.
\nHence, HCF of 106,159 and 265 is 53.<\/p>\n

Continued division method:
\nLet us find the HCF of 106 and 159.
\n\"TS
\nThe HCF of 106 and 159 is 53.
\nLet us find the HCF of 265 and 53.
\n\"TS
\nAgain the HCF of 265 and 53 is 53.
\nSo, the HCF of 106, 159 and 265 is 53.<\/p>\n

(iii) 10, 35, 40
\nAnswer:
\nThe given numbers are 10, 35 and 40.<\/p>\n

Prime factorisation method:
\n\"TS
\n\u2234 The common factor of 10, 35 and 40 is 5.
\nHence, HCF of 10, 35 and 40 is 5.<\/p>\n

Continued division method:
\nThe given numbers are 10, 35 and 40.
\nLet us find the HCF of 10 and 35.
\n\"TS
\n\u2234HCF of 10 and 35 is 5.
\nLet us find the HCF of third number and the HCF of first two numbers.
\nLet us find the HCF of 40 and 5.
\n\"TS
\n\u2234 HCF of 40 and 5 is 5.
\n\u2234 HCF of 10, 35 and 40 is 5.<\/p>\n

\"TS<\/p>\n

(iv) 32, 64, 96, 128
\nAnswer:
\nThe given numbers are 32, 64, 96 and 128.<\/p>\n

Prime factorisation method:
\n\"TS
\n\u2234 The common factor of 32, 64, 96 and 128 is 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 = 32
\n\u2234 HCF of 32, 64, 96 and 128 is 32.<\/p>\n

Continued division method:
\nLet us find the HCF of 32 and 64.
\n\"TS
\n\u2234 HCF of 32 and 64 is 32.
\nAgain find the HCF of 32 and 96.
\n\"TS
\n\u2234 HCF of 32 and 96 is 32.
\nAgain find the HCF of 32 and 128.
\n\"TS
\n\u2234 HCF of 32 and 128 is 32.
\n\u2234 The HCF of the given numbers is 32.<\/p>\n

Question 2.
\nFind the largest number which is a factor of each of the numbers 504, 792 and 1080.
\nAnswer:
\nLargest number which is a factor of the given numbers is HCF.
\nLet us find the HCF of 504 and 792.
\n\"TS
\n\u2234 HCF of 72 and 1080 is 72.
\nThe HCF of 504, 792 and 1080 is 72.<\/p>\n

\"TS<\/p>\n

Question 3.
\nThe length, breadth and height of a room are 12m, 15m and 18m respectively. Determine the length of longest stick that can measure all the dimensions of the room in exact number of times?
\nAnswer:
\nThe HCF of 12, 15 and 18 will give us the length of the stick which can measure all the three dimensions of the room exactly.
\n\"TS
\n\u2234 HCF of 12, 15 and 18 is 3.
\nThe length of stick is 3 m.<\/p>\n

Question 4.
\nHCF of co-prime numbers 4 and 15 was found as follows by factorization. 4 = 2 \u00d7 2 and 15 = 3 \u00d7 5. Since there is no common prime factor, HCE of 4 and 15 is \u20180\u2019. Is the answer correct? If not, what Is the correct HCF?
\nAnswer:
\nThe numbers which have only 1 as the common factor are called co-primes.
\nIn the problem it is given that 4 and 15 are co-prime numbers.
\n\u2234 Their common factor is 1.
\nHCF of 4 and 15 is ‘0’ given in the problem. This is not correct.
\nThe correct HCF is 1.<\/p>\n

Question 5.
\nWhat is the capacity of the largest vessel which can empty the oil from three vessels containing 32 litres, 24 litres and 48 litres an exact number of times ?
\nAnswer:
\nThe quantity of oil in three vessels is 32 litres, 24 litres and 48 litres.
\n\"TS
\n\u2234 LCM = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 2 \u00d7 2 = 96
\nThe capacity 4 the largest vessel = 96 litres.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can practice TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.4 to get the best methods of solving problems. TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Exercise 3.4 Question 1. Find the HCF of the following numbers by prime factorisation and continued division method. (i) 18, 27, 36 … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/8308"}],"collection":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/comments?post=8308"}],"version-history":[{"count":3,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/8308\/revisions"}],"predecessor-version":[{"id":8334,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/8308\/revisions\/8334"}],"wp:attachment":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/media?parent=8308"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/categories?post=8308"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/tags?post=8308"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}