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Chapter 3: Playing With Numbers

    Introduction

    Factors and Multiples

    Prime and Composite Numbers

    Even and Odd numbers

    Tests for Divisibility of Numbers

    Prime Factorisation

    Common Factors and Common Multiples

    Exercise 3.1

    Exercise 3.2

    Exercise 3.3

    Exercise 3.4

    Exercise 3.5

    Exercise 3.6

    Exercise 3.7

    What Have We Discussed?

    Enhanced Curriculum Support

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Chapter 3: Playing With Numbers > Exercise 3.4

Exercise 3.4

Find the common factors of :

Instructions

(a) 20 and 28

Factors of 20 : , , 4 , 5 , ,
Factors of 28 : , 2 , , ,
Therefore, the common factors of 20 and 28 are , and .

(b) 15 and 25

Factors of 15 : , 3 , ,
Factors of 25 : , ,
Therefore, the common factors of 15 and 25 are ,

(c) 35 and 50

Factors of 35 : , 5 , ,
Factors of 50 : , , , 10 ,
Therefore, the common factors of 35 and 50 are ,

(d) 56 and 120

Factors of 56 : , 2 , , , 8 , 14 , ,
Factors of 120 : , , , , 5 , 6 , , , 12 , , 20 , 30 , 40 , ,
Therefore, the common factors of 56 and 120 are , , and

Instructions

1. To find the common factors of multiple numbers, we list the factors of each number and identify the factors they have in common.

Find the common factors

  • For 4, 8 and 12: Factors of 4: is 1, , 4 and Factors of 8: 1, 2, , and Factors of 12: 1, , , 4, , .
  • Common factors are: , , .
  • For 5, 15 and 25: Factors of 5: is 1, and Factors of 15: 1, , 5, and Factors of 25: 1, ,
  • Common factors are: , .

Find first three common multiples of :

(a) 6 and 8 :

Multiples of 6 : 6, 12, , , , , , 48, 54, 60, , .

Mutltipes of 8 : 8, 16, 24, , , 48, , , , 80.

The first three common multiples are: , , .

(b) 12 and 18 :

Multiples of 12: 12, 24, , , 60, , 84, , 108, 120.

Multiples of 18: 18, 36, , , , 108, , , 162, 180.

The first three common multiples are: , , .

Write all the numbers less than 100 which are common multiples of 3 and 4.

The prime factorization of 3 is 31 and 4 is 22.

The LCM is obtained by taking the highest powers of all primes:

LCM(3,4) = 22 × 3 =

Multiples of 12 are : , , , , 60 , , , .

The numbers less than 100 that are common multiples of 3 and 4 are:12, 24, 36, 48, 60, 72, 84, 96.

Which of the following numbers are co-prime?

Instructions

A number is divisible by both 5 and 12. By which other number will that number be always divisible?

Instructions

We have to find another number by which the given number is always divisible.
The common factors of 5 and 12 only 1 therefore they are co-primes a number is divisible by two co-primes, then it is also divisible by their product.
So, 5 × 12 =
Thus the number is always divisible by 60.

A number is divisible by 12. By what other numbers will that number be divisible?

If a number is divisible by 12, it means it is a multiple of 12. To find the other numbers by which it will be divisible, we need to find the factors of 12.

The factors of 12 are 1, , , 4, , and 12.

Therefore, a number that is divisible by 12 will also be divisible by 1, 2, 3, 4, 6, and 12.