{"id":42304,"date":"2023-03-30T14:33:57","date_gmt":"2023-03-30T09:03:57","guid":{"rendered":"https:\/\/icsesolutions.com\/?p=42304"},"modified":"2023-03-31T09:58:51","modified_gmt":"2023-03-31T04:28:51","slug":"ml-aggarwal-class-6-solutions-for-icse-maths-chapter-4-ex-4-1","status":"publish","type":"post","link":"https:\/\/icsesolutions.com\/ml-aggarwal-class-6-solutions-for-icse-maths-chapter-4-ex-4-1\/","title":{"rendered":"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 4 Playing with Numbers Ex 4.1"},"content":{"rendered":"

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 4 Playing with Numbers Ex 4.1<\/h2>\n

Question 1.
\nFill in the blanks:
\n(i) A number having exactly two factors is called a …..
\n(ii) A number having more than two factors is called a ………
\n(iii) 1 is neither ……… nor ………
\n(iv) The smallest prime number is ………
\n(v) The smallest odd prime number is ………
\n(vi) The smallest composite number is ………
\n(vii) The smallest odd composite number is ………
\n(viii)All prime numbers (except 2) are ………
\nSolution:
\n(i) A number having exactly two factors is called a prime number.
\n(ii) A number having more than two factors is called a composite number.
\n(iii) 1 is neither prime nor composite.
\n(iv) The smallest prime number is 2.
\n(v) The smallest odd prime number is 3.
\n(vi) The smallest composite number is 4.
\n(vii) The smallest odd composite number is 9.
\n(viii) All prime numbers (except 2) are odd numbers.<\/p>\n

Question 2.
\nState whether the following statements are ture (T) or false (F):
\n(i) The sum of three odd numbers is an even number.
\n(ii) The sum of two odd numbers and one even number is an even number.
\n(iii) The product of two even numbers is always an even number.
\n(iv) The product of three odd numbers is an odd number.
\n(v) If an even number is divided by 2, the quotient is always an odd number.
\n(vi) All prime numbers are odd.
\n(vii) All even numbers are composite.
\n(viii) Prime numbers do not have any factors.
\n(ix) A natural number is called a composite number if it has atleast one more factor other than 1 and the number itself.
\n(x) Two consecutive numbers cannot be both prime.
\n(xi) Two prime numbers are always co-prime numbers.
\nSolution:
\n(i) False
\n(ii) True
\n(iii) True
\n(iv) True
\n(v) False
\n(vi) False
\n(vii) False
\n(viii) False
\n(ix) True
\n(x) False
\n(xi) True<\/p>\n

Question 3.
\nWrite all the factors of the following natural numbers:
\n(i) 68
\n(ii) 27
\n(iii) 210
\nSolution:
\n(i) 68
\nThe factors of 68 are : 1, 2, 4, 17, 34, 68
\n(ii) 27
\nThe factors of 27 are : 1, 3, 9, 27
\n(iii) 210
\nThe factors of 210 are :
\n1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210<\/p>\n

Question 4.
\nWrite first six multiples of the following natural numbers:
\n(i) 3
\n(ii) 5
\n(iii) 12
\nSolution:
\n(i) 3
\nThe first six multiples of 3 are
\n3, 6, 9, 12, 15, 18
\n(ii) 5
\nThe first six multiples of 5 are
\n5, 10, 15, 20, 25, 30
\n(iii) 12
\nThe first six multiples of 12 are
\n12, 24, 36, 48, 60, 72<\/p>\n

Question 5.
\nMatch the items in column 1 with the items in column 2:<\/p>\n\n\n\n\n\n\n\n\n\n
Column 1<\/strong><\/td>\nColumn 2<\/strong><\/td>\n<\/tr>\n
(i) 15<\/td>\n(a) Multiple of 8<\/td>\n<\/tr>\n
(ii) 36<\/td>\n(b) Factor of 30<\/td>\n<\/tr>\n
(iii) 16<\/td>\n(c) Multiple of 70<\/td>\n<\/tr>\n
(iv) 20<\/td>\n(d) Factor of 50<\/td>\n<\/tr>\n
(v) 25<\/td>\n(e) Multiple of 9<\/td>\n<\/tr>\n
(vi) 210<\/td>\n(f) Factor of 20<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Solution:<\/p>\n\n\n\n\n\n\n\n\n\n
Column 1<\/strong><\/td>\nColumn 2<\/strong><\/td>\n<\/tr>\n
(i) 15<\/td>\n(b) Factor of 30<\/td>\n<\/tr>\n
(ii) 36<\/td>\n(e) Multiple of 9<\/td>\n<\/tr>\n
(iii) 16<\/td>\n(a) Multiple of 8<\/td>\n<\/tr>\n
(iv) 20<\/td>\n(f) Factor of 20<\/td>\n<\/tr>\n
(v) 25<\/td>\n(d) Factor of 50<\/td>\n<\/tr>\n
(vi) 210<\/td>\n(c) Multiple of 70<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Question 6.
\nFind the common factors of :
\n(i) 20 and 28
\n(ii) 35 and 50
\n(iii) 56 and 120
\nSolution:
\n(i) 20 and 28
\nThe factors of 20 are:
\n1, 2, 4, 5, 10, 20 The factors of 28 are:
\n1,2,4,7,14,28
\nThe common factors of 20 and 28 are: 1, 2, 4<\/p>\n

(ii) 35 and 20
\nThe factors of 35 are:
\n1, 5, 7, 35
\nThe factors of 20 are:
\n1, 2, 4, 5, 10, 20
\nThe common factors of 35 and 20 are 1,5<\/p>\n

(iii) 56 and 120
\nThe factors of 56 are:
\n1, 2, 4, 7, 8, 14, 28, 56
\nThe factors of 120 are:
\n1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60,120
\nThe common factors of 56 and 120 are 1, 2, 4,8<\/p>\n

Question 7.
\nFind the common factors of:
\n(i) 4, 8, 12
\n(ii) 10, 30 and 45
\nSolution:
\n(i) The factors of 4 are:
\n1, 2, 4
\nThe factors of 8 are:
\n1, 2, 4, 8
\nThe factors of 12 are:
\n1,2, 3,4, 6, 12
\nThe common factors of 4, 8, 12 are 1, 2, 4<\/p>\n

(ii) 10, 30 and 45 .
\nThe factor of 10 are:
\n1, 2, 5, 10
\nThe factor of 30 are:
\n1, 2, 3, 5, 10, 15, 30
\nThe factor of 45 are:
\n1, 3, 5, 9, 15, 45
\nThe common factors of 10, 30, 45 are 1, 5<\/p>\n

Question 8.
\nWrite all natural numbers less than 100 which are common multiples of 3 and 4.
\nSolution:
\nMultiples of 3 are : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87,
\n90, 93, 96, 99, 102, 105, 108, ……….
\nMultiples of 4 are : 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, ……………
\n\u2234 Common multiples of 3 and 4 are : 12, 24, 36, 48, 60, 72, 84, 96, 108, ………..
\nAll the numbers less than 100 which are common multiples of 3 and 4 are 12, 24, 36, 48, 60, 72, 84 and 96.<\/p>\n

Question 9.
\n(i) Write the odd numbers between 36 and 53.
\n(ii) Write the even numbers between 232 and 251.
\nSolution:
\n(i) The odd numbers between 36 and 53 are:
\n37, 39, 41, 43, 45, 47, 49, 51.
\n(ii) The even numbers between 232 and 251 are: 234, 236, 238, 240, 242, 244, 246, 248, 250.<\/p>\n

Question 10.
\n(i) Write four consecutive odd numbers succeeding 79.
\n(ii) Write three consecutive even numbers preceding 124.
\nSolution:
\n(i) Four consecutive odd numbers succeeding 79 are : 81, 83, 85, 87.
\n(ii) Three consecutive even numbers preceding 124 are : 118, 120, 122.<\/p>\n

Question 11.
\nWhat is greatest prime number between 1 and 15?
\nSolution:
\nThe greatest prime number between 1 and 15 is 13.<\/p>\n

Question 12.
\nWhich of the following numbers are prime?
\n(i) 29
\n(ii) 57
\n(iii) 43
\n(iv) 61
\nSolution:
\n(i) 29
\nWe have, 29 = 1 \u00d7 29
\n\u21d2 29 has exactly two factors 1 and 29 itself.
\n\u2234 29 is a prime number.<\/p>\n

(ii) 57
\nWe have, 57 = 1 \u00d7 57 = 3 \u00d7 19 = 57
\n\u2234 Factors of 57 are 1, 3, 19 and 57
\n\u21d2 57 has more than two factors
\n\u2234 57 is not a prime.<\/p>\n

(iii) 43
\nWe have, 43 = 1 \u00d7 43
\n\u21d2 43 has exactly two factors 1 and 43 itself.
\n\u2234 43 is a prime number.<\/p>\n

(iv) 61
\nWe have, 61 = 1 \u00d7 61
\n\u21d2 61 has exactly two factors 1 and 61 itself.
\n\u2234 61 is a prime number.<\/p>\n

Question 13.
\nWhich of the following pairs of numbers are co-prime?
\n(i) 12 and 35
\n(ii) 15 and 37
\n(iii) 27 and 32
\n(iv) 17 and 85
\n(v) 515 and 516
\n(vi) 215 and 415
\nSolution:
\n(i) 12 and 35
\nThe factors of 12 are 1,2, 3,4, 6, 12
\nThe factors of 35 are 1, 5, 7, 35
\nSince, the common factor of 12 and 35 is 1
\n\u2234 They are co-prime.<\/p>\n

(ii) 15 and 37
\nThe factors of 15 are 1, 3, 5, 15
\nThe factors of 37 are 1, 37
\nThe common factor of 15 and 37 is 1
\n\u2234 They are co-prime.<\/p>\n

(iii) 27 and 32
\nThe factors of 27 are 1, 3, 9, 27
\nThe factors of 32 are 1, 2, 4, 8, 16, 32
\nSince, the common factor of 27 and 32 is 1 They are co-prime<\/p>\n

(iv) 17 and 85
\nThe factors of 17 are 1, 17
\nThe factors of 85 are 1, 5, 17, 85
\nThe common factors of 17 and 85 are 1 and 17
\n\u2234 They are not co-prime because they have more than 1 common factor.<\/p>\n

(v) 515 and 516
\nThe factors of 515 are 1, 5, 103, 515
\nThe factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516
\nSince, the common factor of 515 and 516 are 1 and 5
\n\u2234 So, they are not co-prime.<\/p>\n

(vi) 215 and 415
\nThe factors of 215 are 1, 5, 43, 215
\nThe factors of 415 are : 1, 5, 83, 415
\nSince, the common factor of 215 and 415 are 1 and 5.
\n\u2234 So, they are not co-prime.<\/p>\n

Question 14.
\nExpress each of the following numbers as the sum of two odd primes:
\n(i) 24
\n(ii) 36
\n(iii) 84
\n(iv) 98
\nSolution:
\n(i) 24
\n\u21d2 24 = 5 + 19<\/p>\n

(ii) 36
\n\u21d2 36 = 7 + 29<\/p>\n

(iii) 84
\n\u21d2 84 = 17 + 67<\/p>\n

(iv) 98
\n\u21d2 98 = 19 + 79<\/p>\n

Question 15.
\nExpress each of the following numbers as the sum of twin-primes:
\n(i) 24
\n(ii) 36
\n(iii) 84
\n(iv) 120
\nSolution:
\n(i) 24
\n\u21d2 24 = 11 + 13<\/p>\n

(ii) 36
\n\u21d2 36 = 17 + 19<\/p>\n

(iii) 84
\n\u21d2 84 = 41 + 43<\/p>\n

(iv) 120
\n\u21d2 120 = = 59 + 61<\/p>\n

Question 16.
\nExpress each of the following numbers as the sum of three odd primes:
\n(i) 21
\n(ii) 35
\n(iii) 49
\n(iv) 63
\nSolution:
\n(i) 21
\n\u21d2 21 = 3 + 7 + 11<\/p>\n

(ii) 35
\n\u21d2 35 = 5 + 11 + 19<\/p>\n

(iii) 49
\n\u21d2 49 = 7 + 11 + 31<\/p>\n

(iv) 63
\n\u21d2 63 = 7 + 13 + 43<\/p>\n

ML Aggarwal Class 6 Solutions for ICSE Maths<\/a><\/h4>\n","protected":false},"excerpt":{"rendered":"

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 4 Playing with Numbers Ex 4.1 Question 1. Fill in the blanks: (i) A number having exactly two factors is called a ….. (ii) A number having more than two factors is called a ……… (iii) 1 is neither ……… nor ……… (iv) The smallest prime …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[3034],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/posts\/42304"}],"collection":[{"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/comments?post=42304"}],"version-history":[{"count":1,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/posts\/42304\/revisions"}],"predecessor-version":[{"id":158940,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/posts\/42304\/revisions\/158940"}],"wp:attachment":[{"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/media?parent=42304"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/categories?post=42304"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/tags?post=42304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}