Balbharati Solutions Class 5 Mathematics Multiples and Factors
Welcome to NCTB Solutions. Here with this post we are going to help 5th class students for the Solutions of Balbharati Class 5 Math Book, Problem Set 32, 33, 34 and 35, Multiples and Factors. Here students can easily find step by step solutions of all the problems for Multiples and Factors. Also our Expert Mathematic Teacher’s solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get Multiples and Factors solutions. Here all the solutions are based on Maharashtra State Board latest syllabus.
Multiples and Factors all Question Solutions :
Problem Set 32 :
Question no – (1)
Solution :
Factors of 8
The factors of any number is always 1 and the number itself
Because 1 and the number itself are exactly divisible of that number without remainder
So, 1 and 8 are factors of 8
And also
8 divisible by 2 without any remainder
8 divisible by 4 without any remainder
Therefore, the factors of 8 are 1, 2, 4, 8
Question no – (2)
Solution :
Factors of 5
The factors of any number is always 1 and the number itself
Because 1 and the number itself are exactly divisible of that number without remainder
So, 1 and 5 are factors of 5
So, The factors of 5 are 1 and 5.
Question no – (3)
Solution :
Factors of 14
The factors of any number is always 1 and the number itself
Because, 1 and the number itself are exactly divisible of that number without remainder
So 1 and 14 are factors of 14
And also
14 divisible by 2 any remainder
14 divisible by 7 without any remainder
Thus, the factors of 14 are 1 , 2 , 7 , 14.
Question no – (4)
Solution :
Factors of 10
The factors of any number is always 1 and the number itself
Because, 1 and the number itself are exactly divisible of that number without remainder
So, 1 and 10 are factors of 10
And also
10 divisible by 2 without any remainder
10 divisible by 5 without any remainder
So, the factors of 10 are 1 , 2 , 5 , 10.
Question no – (5)
Solution :
Factors of 7
The factors of any number is always 1 and the number itself
Because, 1 and the number itself are exactly divisible of that number without remainder
So, 1 and 7 are factors of 7
So, the factors of 7 are 1, 7
Question no – (6)
Solution :
Factors of 22
The factors of any number is always 1 and the number itself
Because, 1 and the number itself are exactly divisible of that number without remainder
So, 1 and 22 are factors of 22
And also,
22 divisible by 2 without any remainder
22 divisible by 11 without any remainder
So, the factors of 22 are 1 , 2 , 11 , 22.
Question no – (7)
Solution :
Factors of 25
The factors of any number is always 1 and the number itself.
Because, 1 and the number itself are exactly divisible of that number without remainder.
So, 1 and 25 are factors of 25.
And also
25 divisible by 5 without any remainder.
So, the factors of 25 are 1, 5, 25.
Question no – (8)
Solution :
Factors of 32
The factors of any number is always 1 and the number itself.
Because, 1 and the number itself are exactly divisible of that number without remainder.
So, 1 and 32 are factors of 32.
And also,
32 divisible by 2 without any remainder.
32 divisible by 4 without any remainder.
32 divisible by 8 without any remainder.
32 divisible by 16 without any remainder.
So, the factors of 32 are 1, 2, 4, 8, 16, 32.
Question no – (9)
Solution :
Factors of 33
The factors of any number is always 1 and the number itself.
Because 1 and the number itself are exactly divisible of that number without remainder.
So, 1 and 33 are factors of 33.
And also,
33 divisible by 3 without any remainder.
33 divisible by 11 without any remainder.
So, the factors of 33 are 1, 3, 11, 33.
Problem Set 33 :
Question no – (1)
Solution :
(1) Five three-digit numbers that are multiples of 2
126 is multiple of 2 or exactly divisible by 2 and it is also a three-digit number.
248 is multiple of 2 or exactly divisible by 2 and it is also a three-digit number.
326 is multiple of 2 or exactly divisible by 2 and it is also a three-digit number.
540 is multiple of 2 or exactly divisible by 2 and it is also a three-digit number.
872 is multiple of 2 or exactly divisible by 2 and it is also a three-digit number.
So, the five three-digit numbers that are multiples of 2 are 126, 248, 326, 540, 872.
(2) Five three digit numbers that are multiples of 5
235 is multiple of 5 or exactly divisible by 5 and it is also a three-digit number
610 is multiple of 5 or exactly divisible by 5 and it is also a three-digit number
500 is multiple of 5 or exactly divisible by 5 and it is also a three-digit number
555 is multiple of 5 or exactly divisible by 5 and it is also a three-digit number
840 is multiple of 5 or exactly divisible by 5 and it is also a three-digit number
So, the three-digit numbers that are multiples of 5 are 235, 610, 500, 555, 840.
(3) Five three digit numbers that are multiples of 10
100 is multiple of 10 or exactly divisible by 10 and it is also a three-digit number
200 is multiple of 10 or exactly divisible by 10 and it is also a three-digit number
300 is multiple of 10 or exactly divisible by 10 and it is also a three-digit number
560 is multiple of 10 or exactly divisible by 10 and it is also a three-digit number
870 is multiple of 10 or exactly divisible by 10 and it is also a three-digit number
So, the three-digit number that are multiple of 10 are 100, 200, 300,560, 870.
Question no – (2)
Solution :
342 multiple of 2 as well as 3 or exactly divisible by 2 as well as 3 and it is also a three-digit number
318 multiple of 2 as well as 3 or exactly divisible by 2 as well as 3 and it is also a three-digit number
666 multiple of 2 as well as 3 or exactly divisible by 2 as well as 3 and it is also a three-digit number
246 multiple of 2 as well as 3 or exactly divisible by 2 as well as 3 and it is also a three-digit number
846 multiple of 2 as well as 3 or exactly divisible by 2 as well as 3 and it is also a three-digit number
So, 5 numbers that are multiples of 2 as well as of 3 are 342, 318, 666, 246, 846.
Question no – (3)
Solution :
As we Know, 3 meter means 300 cm
300 cm cut it into 50 cm prices.
Here 300 is exactly divisible by 50.
It means ribbon cut into 6 equal 50 cm pieces.
Therefore, nothing is left in this ribbon.
Question no – (4)
Solution :
As we all Know, 3 meter means 300 cm
1 piece of ribbon is 40 cm
Needed of 8 piece of ribbon means that
40 cm × 8 = 320 cm
320 cm ribbon needed for 8 equal pieces each of 40 cm.
So, ribbon is shorter by = needed ribbon–3 meter long ribbon
Ribbon is shorter by = 320 cm – 300 cm
Ribbon is shorter by = 20 cm
Hence, 20 centimetres shorter is the ribbon than the length need.
Problem Set 34 :
Question no – (1)
Solution :
We know, A number which has only two factors, 1 and the number itself, is called a Prime Number.
2 has only two factors, 1 and 2 hence it is a prime number.
3 has only two factors, 1 and 3 hence it is a prime number.
5 has only two factors, 1 and 5 hence it is a prime number.
7 has only two factors, 1 and 7 hence it is a prime number.
11 has only two factors, 1 and 11 it is a prime number.
13 has only two factors, 1 and 13 hence it is a prime number.
17 has only two factors, 1 and 17 hence it is a prime number.
19 has only two factors, 1 and 19 hence it is a prime number.
Prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19.
Question no – (2)
Solution :
As we know, a number which has more than two factors is called a Composite Number.
22 has more than two factors are 1, 2, 11, 22
24 has more than two factors are 1, 2, 3, 4, 6, 12, 24
25 has more than two factors are 1, 5, 25
26 has more than two factors are 1, 2, 13, 26
27 has more than two factors are 1, 3, 9, 27
28 has more than two factors are 1, 2, 4, 7, 14, 28
30 has more than two factors are 1, 2, 3, 5, 6, 10, 15, 30
32 has more than two factors are 1, 2, 4, 8, 16, 32
33 has more than two factors are 1, 3, 11, 33
34 has more than two factors are 1, 2, 17, 34
35 has more than two factors are 1, 5, 7, 35
36 has more than two factors are 1, 2, 3, 4, 6, 9, 12, 18, 36
38 has more than two factors are 1, 2, 19, 38
39 has more than two factors are 1, 3, 13, 39
40 has more than two factors are 1, 2, 4, 5, 8, 10, 20, 40
42 has more than two factors are 1, 2, 3, 6, 7, 14, 21, 42
44 has more than two factors are 1, 2, 4, 11, 22, 44
45 has more than two factors are 1, 3, 5, 9, 15, 45
46 has more than two factors are 1, 2, 23, 46
48 has more than two factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
49 has more than two factors are 1, 7, 49
So, above number are composite number because above number has multiple factors
Composite numbers between 21 and 50 are 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, and 49.
Question no – (3)
Solution :
- 37 has only two factors, 1 and 37 hence it is a prime number.
- 43 has only two factors, 1 and 43 hence it is a prime number.
- 53 has only two factors, 1 and 53 hence it is a prime number.
- 59 has only two factors, 1 and 59 hence it is a prime number.
- 79 has only two factors, 1 and 79 hence it is a prime number.
- 97 has only two factors, 1 and 97 hence it is a prime number.
Question no – (4)
Solution :
As we know, 2 is a even number
2 has only two factors, 1 and 2 hence it is a prime number
No other even number has only two factors
So, 2 is a prime number which is even number.
Problem Set 35 :
Question no – (1)
Solution :
(1) 22, 24
Factors of 22 are 1,2,11,22
Factors of 24 are 1,2,3,4,6,12, 24
Numbers which have only 1 as a common factor are called co-prime numbers
Here 1 and 2 are two common factors
So , 22,24 pair is not co-prime numbers
(2) 14, 21
Factors of 14 are 1,2,7,14
Factors of 21 are 1,3,7,21
Numbers which have only 1 as a common factor are called co-prime numbers
Here 1 and 7 are two common factors
So, 14, 21 pair is not co-prime numbers.
(3) 10, 33
Factors of 10 are 1, 2, 5, 10
Factors of 33 are 1,11,3, 33
Numbers which have only 1 as a common factor are called co-prime numbers
Here 1 is only one common factors
So , 14,21 pair is co-prime numbers.
(4) 11, 30
Factors of 11 are 1,11
Factors of 30 are 1,2,3,5,6,10,15,30
Numbers which have only 1 as a common factor are called co-prime numbers
Here 1 is only one common factors.
So, 11, 30 pair is co-prime numbers.
(5) 5, 7
Factors of 5 are 1,5
Factors of 7 are 1,7
Numbers which have only 1 as a common factor are called co-prime numbers
Here 1 is only one common factors
Hence, 5, 7 pair is co-prime numbers
(6) 15, 16
Factors of 15 are 1,3,5,15
Factors of 16 are 1,2,4,8,16
Numbers which have only 1 as a common factor are called co-prime numbers
Here 1 is only one common factors
So, 15,16 pair is co-prime numbers.
(7) 50, 52
Factors of 50 are 1,2,5,10,25,50
Factors of 52 are 1,2,4,13,26,52
Numbers which have only 1 as a common factor are called co-prime numbers
Here 1 and 2 are two common factors
Thus, 50,52 pair is not co-prime numbers.
(8) 17, 18
Factors of 17 are 1,17
Factors of 18 are 1,2,3,6,9,18
Numbers which have only 1 as a common factor are called co-prime numbers
Here 1 is only one common factors
Therefore, 17,18 pair is co-prime numbers.
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