**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.

**More Solutions : **

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