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Frank Learning Maths Class 5 Solutions Chapter 6 Multiples and Factors
Welcome to NCTB Solution. Here with this post we are going to help 5th class students for the Solutions of Frank Learning Maths Class 5 Book, Chapter 6 Multiples and Factors. Here students can easily find step by step solutions of all the problems for Multiples and Factors. Here students will find solutions for Exercise 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 and 6.7. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily. Here in this post all Mathematic solutions are based on the CBSE latest curriculum.
Multiples and Factors Exercise 6.1 Solution
Question no – (1)
Solution :
| Table 1 | Table 2 | |
| (a) | 3 | (iii) Factor of 15 |
| (b) | 8 | (iv) Factors of 32 |
| (c) | 7 | (i) Factor of 49 |
| (d) | 5 | (ii) Factor of 25 |
Question no – (2)
Solution :
(a) Yes, 9 is a factor of 36.
(b) The statement is False.
Because, 13 is not a factor of 216
(c) The statement is True.
Yes, 25 is a factor of 125
Question no – (3)
Solution :
(a) Factors of 24 → 1, 2, 3, 4, 6, 8, 12, 24
(b) Factors of 36 → 1, 2, 3, 4, 6, 9, 12, 18, 36
(c) Factors of 80 → 1, 2, 3, 4, 5, 8, 10, 20, 40, 80
(d) Factors of 108 → 1, 2, 3, 4, 6, 9, 12, 18, 136
(e) Factors of 225 → 1, 3, 5, 9, 15, 25, 75, 225
Question no – (4)
Solution :
(a) Common factors of 14, 35 = 1, 7
(b) Common factors of 27, 36 = 1, 3, 9
(c) Common factors of 48, 32 = 1, 2, 4, 8, 16
(d) Common factors of 36, 45 = 1, 3, 9
(e) Common factors of 64, 96 = 1, 2, 4, 8, 16, 32
(d) Common factors of 36, 45 = 1, 3, 9
(e) Common factors of 64, 96 = 1, 2, 4, 8, 16, 32
Question no – (5)
Solution :
The given numbers,
11, 15, 21, 29, 31, 35, 60, 135, 154, 165, 175, 191, 203, 257, 263
∴ Multiples of 7 are –
= 21, 35, 154, 175, 203
Question no – (6)
Solution :
(a) Six multiples of 5 are : 10, 15, 20, 25
(b) Six multiples of 9 are : 18, 27, 36, 45
(c) Six multiples of 11 are : 22, 33, 44, 55
(d) Six multiples of 23 are :46, 69, 92, 115
Question number – (7)
Solution :
(a) 8, 16, 24, 32, 40, 48, 56, 64
(b) 4, 8, 12, 16, 20, 24, 28, 32, 36
Question no – (8)
Solution :
(a) Every number is a multiple of itself.
(b) Every multiple of a number is Greater than or equal to the number.
(c) The number of multiples of a given number is infinite.
(d) The first multiple of every number is itself.
(e) Every number has at least two, (1 and that no.) factors.
(g) The greatest factor of every number is the number itself.
Multiples and Factors Exercise 6.2 Solution
(1) Which among the following numbers are prime?
Solution :
Given numbers are, 36, 37, 31, 59 and 81
Here 37, = 31 and 59 are prime number.
Because, they cannot be factorized.
Question number – (2)
Solution :
(a) 24 = 48, 72, 96, 120
(b) 37 = 74, 148, 222, 296, 370
(c) 58 = 116, 174, 232, 290
(d) 71 = 142, 288, 432, 576
Question number – (3)
Solution :
(a) 11 = 33, 55, 77, 99
(b) 25 = 75, 125, 175
(c) 39 = 117, 195, 273
(d) 67 = 201, 335, 469
Question number – (4)
Solution :
The prime numbers are,
= 23, 29, 31, 37, 41, 43, 47
So, the prime numbers between 20 and 50 are
= 23, 29, 31, 37, 41, 43, 47
Question number – (5)
Solution :
The prime number are, 11, 13, 17, 19, 31, 37
∴ (2) (4) (8) (10) (4) (10) divisible by 2
Question number – (6)
Solution :
Such prime numbers between 1 and 100 are,
∴ The numbers are,
= 13 and 31, (37, 73), 79, 97
Question number – (8)
Solution :
The numbers are
= (23, 29), (31, 37), (47, 53)
Question number – (9)
Solution :
All twin primes between 1 and 100 are –
= (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), 41, 43 (59, 61), 71, 73
Question number – (10)
Solution :
Co-primes are,
(b) 24 and 29
(c) 34 and 57
(d) 18 and 67
Because, they cannot divided the same number.
Multiples and Factors Exercise 6.3 Solution
Question number – (1)
Solution :
| Given number | Divisible by | |||||||
| 2 | 3 | 4 | 5 | 6 | 8 | 9 | 10 | |
| 1218 | ✓ | ✓ | × | × | ✓ | × | × | × |
| 8232 | ✓ | ✓ | ✓ | × | ✓ | ✓ | × | × |
| 5920 | ✓ | × | ✓ | ✓ | × | ✓ | × | ✓ |
| 2928 | ✓ | ✓ | ✓ | × | ✓ | ✓ | × | × |
| 4644 | ✓ | ✓ | ✓ | × | ✓ | × | ✓ | × |
| 48438 | ✓ | ✓ | × | × | ✓ | × | ✓ | × |
Question no – (2)
Solution :
Given numbers,
(a) 4623 (b) 9000 (c) 1438
(d) 7596 (e) 8875 (f) 20014
As we know,
If the last digit of the number is 0, 2, 4, 6, and 8 then the number is divisible by 2
Here the number is 9000 (last digit of the number is 0)
So, it is divisible by 2
So, now we can say that 9000, 1438, 7596 and 20014 is divisible by 2.
And 4623 and 8875 is not divisible by 2.
Question no – (3)
Solution :
Given numbers,
(a) 3123 (b) 4826 (c) 52596
(d) 76321 (e) 84463
As We know that,
A number is divisible by 3 if the sum of digits is divisible by 3
Here, in the question the number is 474
So, 3123 = 3 + 1 + 2 + 3 = 9
9 is divisible by 3
So, 3123 is divisible by 3.
Now, we can say that, 3123 and 52596 is divisible by 3.
And 4826, 76321 and 84463 are not divisible by 3.
Question number – (4)
Solution :
Given numbers,
(a) 486 (b) 512 (c) 4920
(d) 7773 (e) 9636 (f) 58862
As we know that,
A number is divisible by 4 if the last two digit of the number is divisible by 4 or the whole number is divisible by 4
Here, in the question the number is 512
last two digit 12 ÷ 4 = 3
and also the whole number 512 ÷ 4 = 128
So, 512 is divisible by 4
Now, we can say that, 512, 4920 and 9636 are divisible by 4.
And 486, 7773 and 58862 are not divisible by 4.
Question number – (5)
Solution :
Given numbers,
(a) 5912 (b) 7732 (c) 9008
(d) 46246 (e) 83224
As we know that,
A number is divisible by 8 if its last three digits are divisible by 8 then the number is divisible by 8
Here, in the question the number is 5912
last three digit 912 ÷ 8 = 114
and also the whole number 5912 ÷ 8 = 739
So, 7304 is divisible by 8
Now, we can say that, 5912, 9008 and 83224 are divisible by 8
And 7732 and 46246 is not divisible by 8.
Question no – (6)
Solution :
Given numbers,
(a) 6987 (b) 8424 (c) 9405
(d) 50049 (e) 68978
As we know that,
A number is divisible by 9 if the sum of all digits is divisible by 9
Here, in the question the number is 2358
So, 8424 = 8 + 4 + 2 + 4 = 18
18 is divisible by 9
So, 8424 is divisible by 9.
Now, we can say that 8424, 9405 and 50048 is divisible by 9.
And 6987 and 68978 is not divisible by 9.
Question number – (7)
Solution :
(a) 15921,
(b) 8022,
(c) 5916,
(d) 52251
Now, these number is divisible by 3.
Question number – (8)
Solution :
As we know that,
A number is divisible by 4 if the last two digit of the number is divisible by 4 or the whole number is divisible by 4.
(a) 49508
(b) 34012
(c) 54252
(d) 39272
Now, the digits are divisible by 4.
Question number – (9)
Solution :
As we know,
A number is divisible by 8 if its last three digits are divisible by 8 then the number is divisible by 8.
(a) 3656
(b) 37264
(c) 63784
(d) 8312
These digits are divisible by 8.
Because, now the last three digit are divisible by 8.
Question number – (10)
Solution :
As we know,
A number is divisible by 9 if the sum of all digits is divisible by 9.
(a) 5724
(b) 47358,
(c) 19755
(d) 4212
Now, these digits are divisible by 9.
Because, the sum of the digit are divisible by 9.
Multiples and Factors Exercise 6.4 Solution
Question no – (1)
Solution :
(a) 24, 33
24 = 2 × 2 × 3 × 2
33 = 3 × 11
HCF of 24 and 33 = 3
(b) 36, 252
36 = 2 × 2 × 3 × 3
252 = 2 × 2 × 3 × 3 × 7
HCF = 3 × 3 × 2 × 2
= 36
(c) 18, 36, 45
18 = 2 × 3 × 3
36 = 2 × 2 × 3 × 3
45 = 3 × 3 × 5
HCF = 3 × 3 = 6
(d) 45, 25, 65
45 = 3 × 3 × 5
25 = 5 × 5
65 = 5 × 13
HCF = 5
Question no – (2)
Solution :
(a) 42, 84
42 = 2 × 3 × 7
84 = 2 × 2 × 3 × 7
HCF = 2 × 3 = 6
(b) 36, 63
36 = 2 × 2 × 3 × 3
63 = 3 × 3 × 7
HCF = 3 × 3 = 9
(c) 25, 90
25 = 5 × 5
90 = 2 × 3 × 3 × 5
HCF = 5
(d) 12, 18, 27
12 = 2 × 2 × 3
18 = 2 × 3 × 3
27 = 3 × 3 × 3
HCF = 3
(e) 18, 24, 32
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
32 = 2 × 2 × 2 × 2 × 2
HCF = 2
(f) 22, 66, 121
22 = 2 × 11
66 = 6 × 11
121 = 11 × 11
HCF = 11
(g) 25, 65, 95
25 = 5 × 5
65 = 5 × 13
95 = 5 × 18
HCF = 5
(h) 64, 80, 120
64 = 2 × 2 × 2 × 2 × 2 × 2
80 = 2 × 2 × 2 × 2 × 5
120 = 2 × 2 × 2 × 3 × 5
HCF = 2 × 2 × 2 = 8
Question no – (3)
Solution :
(a) 12, 28
So, the HCF is 4
(b) 42, 330
So, the HCF is 6
(c) 78, 210
So, the HCF is 6
(d) 60, 420, 924
So, the HCF is 12
Multiples and Factors Exercise 6.5 Solution
Question no – (1)
Solution :
(a) 30, 75
LCM = 3 × 5 × 2 × 5
= 150
(b) 45, 66
LCM = 3 × 15 × 22
= 990
(c) 20, 25, 60
LCM = 5 × 2 × 2 × 5 × 3
= 300
(d) 36, 63, 81
LCM = 3 × 3 × 4 × 7 × 9
= 2268
Question no – (2)
Solution :
(a) Given number, 28 and 35
28 = 2 × 2 × 7
35 = 5 × 7
∴ LCM = 7 × 2 × 2 × 5
= 140
(b) Given number, 48 and 72
48 = 2 × 2 × 2 × 2 × 3
72 = 2 × 2 × 2 × 3 × 3
∴ LCM = 2 × 2 × 2 × 3 × 2 × 3
= 144
(c) Given number, 22 and 66
22 = 2 × 11
66 = 11 × 2 × 3
∴ LCM = 11 × 2 × 3
= 66
(d) Given number, 36, 48 and 96
36 = 2 × 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
96 = 2 × 2 × 2 × 2 × 3
∴ LCM = 2 × 2 × 3 × 3 × 2 × 2 × 2
= 288
(e) Given number, 125, 180 and 210
125 = 5 × 5 × 5
180 = 3 × 3 × 4 × 5
210 = 3 × 2 × 7 × 5
∴ LCM = 5 × 5 × 5 × 3 × 3 × 2 × 2 × 7
= 31,500
Question no – (3)
Solution :
(a) Given number, 20, 35, and 45
Now, by common division method,
∴ LCM = 5 × 4 × 7 × 9
= 1260
So, the LCM of 20, 35, and 45 is 1260.
(b) 10, 25, 65
∴ LCM = 5 × 2 × 5 × 13
= 650
(c) 27, 45, 60, 72, 96
∴ LCM = 3 × 3 × 2 × 2 × 2 × 5 × 3 ×4
= 4320
(d) 36, 64, 72, 36, 120
∴ LCM = 2 × 2 × 2 × 3 × 2 × 3 × 2 × 2 × 5
= 2880
(e) 42, 60, 84, 108
∴ LCM = 2 × 3 × 2 × 7 × 5 × 9
= 3780
(f) 135, 175
∴ LCM = 5 × 27 × 35
= 4725
(g) 144, 120
∴ LCM = 2 × 2 × 2 × 3 × 6 × 5
= 720
Multiples and Factors Exercise 6.6 Solution
Question number – (1)
Solution :
Here, numbers we find, 8, 15, 24
Now,
∴ LCM,
= 2 × 4 × 3 × 5
= 120
So, the smallest number is = 120
Question number – (2)
Solution :
= 2 × 3 × 2 × 3 × 2
= 72
∴ The required number,
= (72 + 7)
= 79
So, the required least number is 79
Question number – (3)
Solution :
Given numbers, 12, 16, 24 and 36
∴ LCM
= 2 × 2 × 3 × 2 × 2 × 3
= 144
∴ Required number,
= 144 + 5
= 149
So, the required least number is 149
Question number – (4)
Solution :
In the question,
The greatest number which exactly divides 27 and 33
So, the greatest number is 3
Question number – (5)
Solution :
Given numbers, 48, 60 and 64
Now,
∴ The number = 4
So, the Required largest number is 4.
Question number – (6)
Solution :
Given numbers, 368, 480 and 536.
Now,
∴ The number is = 8
So, the required greatest number is 8.
Question number – (7)
Solution :
Given numbers, 9, 12 and 15
Now,
9 = 3 × 3
12 = 2 × 2 × 3
15 = 5 × 3
∴ HCF = 3
So, they tell together after 3 minutes.
Question number – (8)
Solution :
Given numbers,
25 cm, 40 cm and 60 cm
Now,
∴ LCM,
= 2 × 2 × 5 × 5 × 2 × 3
= 600
∴ The distance = 600 cm.
So, they taking steps together again in 600 cm.
Question number – (9)
Solution :
∴ Number of student = 36
So, each student will get 36 chocolates and cookies.
Question number – (10)
Solution :
Acceding to the question,
4 m 25 cm = 425 cm
5 m 50 cm = 550 cm
6 m = 600 cm
∴ Length of the longest tape is 25 cm.
Question number – (11)
Solution :
In the question,
50 rupees = 50,00 paise
₹ 1.25 = 125 paise
Now,
∴ The least number of days is 40
Previous Chapter Solution :
👉 Chapter 5 👈
