## Chapter 8 - Multiples and Factors

**Practice Set 32**

**Write the factors of the following numbers.**

**(1) 8 ****Solution:**

Factors of 8 – 1, 2, 4, 8**(2) 5 ****Solution:**

Factors of 5 – 1, 5**(3) 14****Solution:**

Factors of 14 – 1, 2, 7, 14**(4) 10 ****Solution:**

Factors of 10 – 1, 2, 5, 10**(5) 7 ****Solution:**

Factors of 7 – 1, 7 **(6) 22 ****Solution:**

Factors of 22 – 1, 2, 11, 22**(7) 25 ****Solution:**

Factors of 25 – 1, 5, 25**(8) 32 ****Solution:**

Factors of 32 – 1, 2, 4, 8, 16, 32**(9) 33****Solution:**

Factors of 33 – 1, 3, 11, 33

**Practice Set 33**

**Practice Set 33**

**1. (1) Write five three-digit numbers that are multiples of 2.****Solution:**

Five three-digit numbers that are multiples of 2 are;

(i) 124

(ii) 280

(iii) 552

(iv) 786

(v) 928**(2) Write five three-digit numbers that are multiples of 5.****Solution:**

Five three-digit numbers that are multiples of 5 are;

(i) 105

(ii) 290

(iii) 385

(iv) 470

(v) 565**(3) Write five three-digit numbers that are multiples of 10.****Solution:**

Five three-digit numbers that are multiples of 5 are;

(i) 720

(ii) 300

(iii) 940

(iv) 180

(v) 760

** **

**2. Write 5 numbers that are multiples of 2 as well as of 3.****Solution:**

5 numbers that are multiples of 2 as well as 3 are:

(i) 12

(ii) 30

(iii) 48

(iv) 66

(v) 90

**3. A ribbon is 3 metres long. Can we cut it into 50 cm pieces and have nothing left over ? Write the reason why or why not.****Solution:**

We know that

3 m = 300 cm

To know whether it can cut it into 50 cm pieces or not,

We’ll divide 300 by 50

∴ \( \frac{300}{50} \) = 6

We will get 6 equal pieces and nothing is left over.**Ans**: We cut it into 50 cm pieces and have nothing left over.**4. A ribbon is 3 metres long. I need 8 pieces of ribbon each 40 cm long. How many centimetres shorter is the ribbon than the length I need?****Solution:**

I need 1 piece of 40 cm

So for 8 pieces, I’ll require 40 x 8 = 320 cm of ribbon

We know that 3 m = 300 cm

But the ribbon is 300 cm long.

So the ribbon is shorter by 320 – 300 = 20 cm**Ans**: The ribbon is shorter by 20 cm.**5. If the number given in the table is divisible by the given divisor, put ✓ in the box. If it is not divisible by the divisor, put 5 in the box**.

**Solution:**

**Practice Set 34**

**Practice Set 34****1. Write all the prime numbers between 1 and 20.****Solution:**

Prime numbers between 1 and 20 are;

2, 3, 5, 7, 11, 13, 17, 19.**2. Write all the composite numbers between 21 and 50.****Solution:**

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, 49.**3. Circle the prime numbers in the list given below.****22, 37, 43, 48, 53, 60, 91, 57, 59, 77, 79, 97, 100****Solution:**

**4. Which of the prime numbers are even numbers ?****Solution:**

There is only one prime number that is also an even number, which is “2”.

**Practice Set 35**

**Practice Set 35****Determine whether the pairs of numbers given below are co-prime numbers.**

**(1) 22, 24 ****Solution:**

Factors of 22 – 1, 2, 11, 22

Factors of 24 – 1, 2, 3, 4, 6, 8, 12, 24

Common Factors – 1, 2**∴ 22 and 24 are not coprime numbers.****(2) 14, 21 ****Solution:**

Factors of 14 – 1, 2, 7, 14

Factors of 21 – 1, 3, 7, 21

Common Factors – 1, 7**∴ 14 and 7 are not co-prime numbers.****(3) 10, 33 ****Solution:**

Factors of 10 – 1, 2, 5, 10

Factors of 33 – 1, 3, 11, 33

Common Factor – 1**∴ 10 and 33 are coprime numbers.****(4) 11, 30****Solution:**

Factors of 11 – 1, 11

Factors of 30 – 1, 2, 3, 5, 6, 10, 15, 30

Common Factor – 1**∴ 11 and 30 are coprime numbers.****(5) 5, 7 ****Solution:**

Factors of 5 – 1, 5

Factors of 7 – 1, 7

Common Factor – 1**∴ 5 and 7 are coprime numbers.****(6) 15, 16 ****Solution:**

Factors of 15 – 1, 3, 5, 15

Factors of 16 – 1, 2, 4, 8, 16

Common Factor – 1**∴ 15 and 16 are coprime numbers.****(7) 50, 52****Solution:**

Factors of 50 – 1, 2, 5, 10, 25, 50

Factors of 52 – 1, 2, 4, 13, 26, 51

Common Factors – 1, 2**∴ 50 and 52 are not coprime numbers.****(8) 17, 18****Solution:**

Factors of 17 – 1, 17

Factors of 18 – 1, 2, 3, 6, 9, 18

Common Factor – 1**∴ 17 and 18 are coprime numbers.**