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SEBA Class 6 Mathematics Chapter 2 Types of Numbers
Also, you can read the SCERT book online in these sections Solutions by Expert Teachers as per SCERT (CBSE) Book guidelines. SEBA Class 6 General Mathematics Textual Question Answer. These solutions are part of SCERT All Subject Solutions. Here we have given SEBA Class 6 Mathematics Chapter 2 Types of Numbers Solutions for All Subject, You can practice these here.
Types of Numbers
Chapter – 2
| Try these yourself |
Q.1. Write the factors of each of the following numbers.
(a) 45
Ans: The factors of 45 are 1, 3, 5, 9, 15, 45 [Number of factors = 6].
(b) 60
Ans: The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 [Number of factors = 12].
Q.2. Write first 4 multiples of each of the following numbers.
(a) 6.
Ans: 4 multiples of 6 are 6, 12, 18, 24….
(b) 11.
Ans: 4 multiples of 11 are 11, 22, 33,44,….
(c) 73.
Ans: 4 multiples of 73 are 73, 146, 219, 292….
Q.3. Write the following numbers as the product of 3 factors.
(a) 288.
Ans: 288 = 2 × 144
288 = 4 × 72
288 = 6 × 48
(b) 384.
Ans: 384 = 6 × 64
384 = 2 × 192
384 = 8 × 48
(c) 480.
Ans: 480 = 5 × 96
480 = 2 × 240
480 = 3 × 160
Q.4. Write the multiples of 7 which are in between 30 and 100.
Ans: The multiples of 7 which are in between 30 and 100 are 35, 42, 49, 56, 63, 70, 77, 84, 91.
Q.5. Write the multiples of 17 which are in between 80 and 170.
Ans: The multiples of 17 which are in between 80 and 170 are 85, 102, 119, 136, 153.
Q.6. Write the multiples of 19 which are in between 50 and 190.
Ans: The multiples of 19 which are in be- tween 50 and 190 are 57, 76, 95, 114, 133, 152, 171.
Q.7. The following questions have four answers each tick (✔) the correct one.
(i) First four multiples of 5 are-
(a) 10, 15, 20, 25
(b) 30, 35, 40, 45
(c) 5, 15, 25, 35
(d) 5, 10, 15, 20.
Ans: (d) 5, 10, 15, 20
(ii) Total number of factors of 25 is-
(a) 2
(b) 3
(c) 4
(d) 5
Ans: (b) 3
(iii) Number of multiples of 8 is-
(a) 3
(b) 4
(c) 10
(d) Innumerable.
Ans: (d) Innumerable.
(iv) The factors of 6 are:
(a) 1, 6
(b) 2, 3
(c) 2, 3, 6
(d) 1, 2, 3, 6
Ans: (d) 1,2,3,6
Q.8. Which of the following pairs are co-prime?
(a) 15 and 17
(c) 30 and 415
(b) 18 and 81
(d) 112 and 113
Ans: (a) 15 and 17,
(d) 112 and 113 are co-prime.
Q.9. A number is divisible by 3 and 8. By what other numbers will that number be divisible?
Ans: 24 is divisible by 3 and, 8. It is also divisible by 2, 4, 6, 12.
Q.10. A number is divisible by 15. By which other numbers will that number be divisible?
Ans: 30 is divisible by 15. It is also divisible by 2, 3, 5, 6,10.
Q.11. Examine whether the numbers is prime or not.
(a) 101
Ans: Prime.
(b) 117
Ans: 173 ÷ 39,3 and 9, 13
∴ 117 Not Prime.
(c) 233
Ans: Prime
Test of Divisibility:
Divisibility Rule from 2 to 13
| Exercise – 2B |
Q.1. Which of the following numbers are divisible by (i) 2, (ii) 5 and (iii) 10?
(a) 3,656
(b) 4,608
(c) 23,040
(d) 47,215
Ans: (i) Numbers are divisible by 2 are-
(a) 3,656; (b) 4,608; (c) 23,040.
(ii) Numbers are divisible by 5 are-
(d) 47,215
(iii) Number are divisible by 10 are- (c) 23,040
Q. 2. Which of the following numbers are divisible by 4?
(a) 7004
(b) 9,208
(c) 7,218
(d) 3,000
Ans: Numbers divisible by 4 are- (a) 7004; (b) 9,208; (d) 3,000
Q.3. Which of the following numbers are divisible by 8?
(a) 1,238
(b) 2,408
(c) 4,316
(d) 4,000
Ans: Numbers divisible by 8 are- (b) 2,408; (d) 4,000
Q. 4. Which of the following numbers are divisible by 3?
(a) 780
(b) 4,752
(c) 3,576
(d) 86,732
Ans: Numbers divisible by 3 are- (a) 780; (b) 4,752; (c) 3,576
Q. 5. Which of the following numbers are divisible by 9?
(a) 2,300
(b) 9,126
(c) 8,001
(d) 1,234
Ans: Numbers divisible by 9 are- (b) 9,126; (c) 8,001
Q. 6. Which of the following numbers are divisible by 11?
(a) 7,007
(b) 77,987
(c) 94,325
(d) 8,08,391
Ans: Numbers divisible by 11 are- (a) 7,007; (c) 94,325; (d) 8,09,391
Q. 7. Which of the following numbers are divisible by 6?
(a) 3,484
(b) 30,282
(c) 72,006
(d) 34,560
Ans: Numbers divisible by 6 are- (b) 30,282; (c) 72,006; (d) 34,560.
| Exercise – 2C |
Q.1. Find the Prime Factorisation of the following numbers.
(a) 80
Ans:
80
80 = 2 x 2 x 2 x 2 x 5
∴ The prime factors of 80 are 2, 2, 2, 2,5.
(b) 100
Ans:
100
100 = 2 x 2 x 5 x 5
∴ The prime factors of 100 are 2, 2, 5, 5.
(c) 124
Ans:
124
124 = 2 x 2 x 31
∴ The prime factors of 124 are 2, 2, 31.
(d) 325
Ans:
325
325 = 5 × 5 × 13
∴ The prime factors of 325 are 5, 5, 13.
(e) 915
Ans:
915
915 = 5 × 3 × 61
∴ The prime factors of 915 are 5, 3, 61.
Q.2. Find the common factors of:
(a) 8,20
Ans: 8, 20
Factors of 8 = 1, 2, 4, 8
and factors of 20 = 1, 2, 4, 5, 10, 20
∴ The common factors of 8, 20 are 1, 2, 4
(b) 9, 15
Ans: 9, 15
Factors of 9 = 1, 3, 9
and factors of 15 = 1, 3, 5, 15
∴ The common factors of 9, 15 = 1, 3
(c) 35,50
Ans: 35, 50
Factors of 35 = 1, 5, 7, 35
and factors of 50 = 1, 2, 5, 10, 50
∴ The common factors of 35 and 50 = 1, 5
(d) 56, 120
Ans: 56, 120
∴ The factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
and factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
∴ The common factors of 56 and 120 = 1, 2, 4, 8
Q.3. Find the common factors of:
(a) 5, 15, 25
Ans: 5, 15, 25
Factors of 5 = 5
Factors of 15 = 1, 3, 5, 15
and factors of 25 = 1, 5, 25
∴ The common factors of 5, 15 and 25 = 1, 5
(b) 12, 16, 18
Ans: 12, 16, 18
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 16 = 1, 2, 4, 8, 16
and factors of 18 = 1, 2, 3, 6, 9, 18
∴ The common factors of 12, 16 and 18 = 1, 2
(c) 8, 16, 24
Ans: 8, 16, 24
Factors of 8 = 1, 2, 4, 8
Factors of 16 = 1, 2, 4, 8, 16
and factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
∴ The common factors of 8, 16 and 24 = 1, 2, 4, 8
(d) 9, 15, 21
Ans: 9, 15, 21
Factors of 9 = 1, 3, 9
Factors of 15 = 1, 3, 5, 15
and factors of 21 = 1, 3, 7, 21
∴ Common factors of 9, 15, 21 = 1, 3
Q.4. Find the first 4 common multiples of:
(a) 3, 6
Ans: 3, 6
Multiples of 3 are = 3 ,6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45 …
Multiples of 6 are = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90 …
∴ First 4 common multiples of 3 and 6 are = 6, 12, 18, 24
(b) 5, 10
Ans: 5, 10
Multiples of 5 are = 5,10,15,25,30,35,40,45, 50, 55 …
Multiples of 10 are = 10,20,30,40,50,60,70, 80, 90, 100 …
∴ First 4 common multiples of 5 and 10 are = 10, 20, 30, 40
(c) 8, 12
Ans: 8, 12
Multiples of 8 are = 8, 16, 24, 32, 40, 48, 56, 64 72, 80, 88, 96 …
Multiples of 12 are = 12, 24, 36, 48, 60, 72, 84 96, 108 …
∴ First 4 common multiples of 8 and 12 are = 24, 48, 72, 96
(d) 12, 18
Ans: 12, 18
Multiples of 12 are = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144 …
Multiples of 18 are = 18, 36, 54, 72, 90,108, 126, 144 …
∴ First 4 common multiples of 12 and 18 are = 36, 72, 108, 144
| Exercise – 2D |
Q.1. Find the HCF of the following by using Prime Factorisation method:
(a) 36, 84
Ans: 36, 84
36 = 2 x 2 x 3 x 3
84 = 2 x 2 x 3 x 7
Common prime factors of 36 and 84 are 2, 2 and 3
∴ HCF of 36 and 84 = 2 × 2 × 3 = 12
(b) 34, 102
Ans: 34, 102
34 = 2 × 17
102 = 2 × 3 × 17
∴ H.C.F. of 34 and = 2 × 17 = 34
(c) 91, 112, 49
Ans: 91, 112, 49
91 = 13 x 7
112 = 2 x 2 x 2 x 7
49 = 7 x 7
∴ Common prime factors of 91, 112 and 49 are 7.
∴ H.C.F of 91, 112 and 49 = 7.
Q.2. Find the HCF of the numbers given in question 1, by using the method of common factors.
Ans: (a) 36, 84
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
∴ H .C.F. = 12
(b) 34, 102
Factors of 34 = 1, 2, 17, 34
∴ Factors of 102 = 1, 2, 3, 6, 17, 34, 51, 102
∴ H .C.F. = 34
(c) 91, 112, 49
Factors of 91 = 1, 7, 13, 91
Factors of 112 = 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Factors of 49 = 1, 7, 49
∴ H .C.F. = 7
(d) 18, 54, 81
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 54 = 1, 2, 6, 9, 18, 27, 54
Factors of 81 = 1, 3, 9, 27, 81
∴ H.C.F = 9
(e) 12, 45, 75
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 45 = 1, 3, 5, 9, 15, 45
Factors of 75 = 1, 3, 5, 15, 25, 75
∴ H.C.F. = 3
Q.3. Find the multiples of 8 and 12 within 1 and 100. From the list of multiples find the common multiples of 8 and 12. Then find the LCM of 8 and 12.
Ans: Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96
∴ Common multiples of 8 and 12 are 24, 48, 72, 96.
Lowest Common multiple of two number is 24
∴ Required L.C.M. = 24.
Q.4. Find LCM by using short division method.
(i) 12, 16, 18
Ans: 12, 16, 18
∴ Required L.C.M. = 2 x 2 x 3 x 1 x 4 x 3 = 144
(ii) 20, 25, 30
Ans: 20, 25, 30
∴ Required. L.C.M. = 5 x 2 x 2 x 5 x 3 = 300
(iii) 24, 40, 64
Ans: 24, 40, 64
∴ Required L.C.M. = 2 x 2 x 2 x 3 x 5 x 8 = 960
Q.5. Product of the HCF and LCM of two numbers is 720. If one of the numbers is 30, find the other number.
Ans: Let the other Number be X
One number = 30
HCF x LCM = 720
Product of the HCF and LCM of two numbers = 720
HCF × LCM = 720
30 .x X = 720
X = 720\30
X = 24
Q.6. Find the smallest 4-digit number which is divisible by 18, 24 and 32.
Ans:
∴ L.C.M. = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288
∴ Multiples of 288 = 288 × 1 = 288 ,288 × 2 = 576, 288 × 3 = 846, 288 × 4 = 1152 ……..
∴ The smallest 4-digit number = 1152.
Q. 7. Three men step off together from the same spot. Their steps measure 63 cm, 70 cm, and 77 cm respectively. What is the minimum distance each should cover to meet at a same spot again so that all can cover the distance in complete steps?
Ans:
∴ L.C.M. of 63, 70 and 77 = 2 × 3 × 3 × 5 × 7 × 11 = 6930
∴ The required minimum distance = 6930 cm.
Q.8. Find the greatest number which when divides 35, 45 and 50 leaves no remainder.
Ans: Factors of 35 = 1, 5, 7 and 35
Factors of 45 = 1, 3, 5, 9, 15 and 45
Factors of 50 = 1, 2, 5, 10, 25 and 50
∴ H.C.F. = 5
∴ The greatest number = 5
Q.9. Three drums of a milkman contain 180 litres, 264 litres and 252 litres of milk respectively. Find the maximum capacity of a container that can measure the milk of all the three drums without leaving any milk in the drum.
Ans: Factors of 180 = 1, 2, 3, 6, 9, 10, 12, 15, 18, 20, 30, 60, 90 and 180.
Factors of 264 = 1, 2, 4, 6, 8, 12, 22, 33, 44, 66, 132 and 264.
Factors of 252 = 1, 2, 3, 4, 6, 9, 12, 21, 28, 42, 63, 84, 126 and 252.
∴ H.C.F. = 12
∴ The maximum capacity of a container = 12 litres.
Q.10. A teacher was given 66 bananas and 110 mangoes. Find the maximum number of boys to whom the fruits can be divided equally.
Ans: Factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66
Factors of 110 = 1, 2, 5, 10, 11, 22, 55, 110
∴ Greatest common factor = 22
∴ H.C.F. of 66 and 110 = 22
∴ The maximum number of boys to whom the fruits can be divided equally = 22.
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