﻿ Greatest Common Divisor

# KCSE ONLINE

## One stop Education solutions

### Revision

Other

Candidate benefit from our revision notes which are comprehensive and show how to tackle examination questions effectively

### Results

Moreover

As a supplementary to coursework content our e-library for digitized multimedia CDs while enhance and ensure that you never missed that important concept during the normal class lessons. It is a Do it Yourself Project

### KNEC

For Best results INSTALL Adobe Flash Player Version 16 to play the interactive content in your computer. Test the link below to find out if you have Adobe Flash in your computer

## Greatest Common Divisor

GREATEST COMMON DIVISOR (G.C.D)

BACKGROUND KNOWLEDGE

Find out common factors (Common divisors)

GREATEST COMMON DIVISOR (G.C.D)

BACKGROUND KNOWLEDGE

Find out common factors (Common divisors)

Factor - If a number can be divided by another number

without a remainder, the second number is a factor of the first.

Worked out examples

Find the divisors/ factors of the following set of numbers;

1. 20, 32

2. 36, 48, 60

3. Divisibility test for prime numbers, that is 2,3,5,11

A number is divisible by:

2 - If the last digit is zero or even e.g 30,102, 6, 76

3 - If the sum of the digits are divisible by 3 ,

for example

1 2 3 .........{1+ 2 + 3 = 6}

3 4 5 ........ { 3 + 4 + 5 = 12}

2 0 4 .........{ 2 + 0 + 4 = 6}

5- If the last digit is 0 or 5 e.g. 50, 65, 70

11 - If the last sum of the alternate digit are equal

or their difference is a multiple of 11,

e.g 1 8 7 ...... ( 1 +7) - 8= 0

8 1 9 3 9....{8 + 9 + 9} -{1 +3} = 22

Lesson Objective(s)

#### By the end of this lesson you should be able to

;

apply G.C.D to real life situations appropriately.

GREATEST COMMON DIVISOR (G.C.D)

Introduction

G.C.D/H.C.F can also be determined by using prime factorization

The Greatest Common Divisors (G.C.D) is also refered to as the Highest Common Factors (H.C.F) .The H.C.F of two natural numbers is the largest factor that they have in common.for example, the prime factorisation of 144 and 66 are:

144 = 2 x 2 x 2 x 2 x 3 x 3

66 = 2 x 3 x11

Only 2 and 3 are common to both factorisation and so the the highest common factor that these two number have in common (HCF) is 2 x3 = 6

To find G.C.D/H.C.F of a set of numbers using factorisation:

i). Express each number as a product of prime factor ii). Find the common prime factors iii). multiply the common prime factors together to give GCD/H.C.F

Find the G.C.D/H.C.F for the following set: { 60,90,135 }

60= 2x 2 x 3x 5

90= 2x3x 3x5

135= 3x3x 3 x5

Common prime factors are 3 and 5

G.C.D/H.C.F= 3 x 5 = 15

The concept of G.C.D/H.C.F is applicable in many real life situations:

Given two containers of capacity 20 litres and 30 litres respectively. Find the capacity of largest jug that can be used to fill each of containers exactly.

Solution

20 = 2 x 2 x 5 ,

30 = 2 x 3 x 5

Common factors are 2 and 5

G.C.D = 2 X 5 = 10

Four ribbons of colours red , blue green and yellow of lengths 18m, 24m, 36m and 42 m respectively are to be used for wrapping a number of birthday gifts. The owner wishes to cut them into shorter pieces of equal length. find the greatest possible length if no ribbon is left over.

Solution

Write the numbers 18,24,36 and 42 as a product of their prime factors

18 = 2 x 3 x 3

24 = 2 x 2 x 2 x 3

36 = 2 x 2 x 3 x 3

42= 2 x 3 x 7

The common factors are 2 and 3

The G.C.D is 2 x 3 = 6 . Therefore the greatest possible length is 6m

3. Divisibility test for prime numbers, that is2,3,5,11

A number is divisible by:

2 - If the last digits is zero or even e.g 30,102, 6, 76

3 - If the sum of the digits are divisible by 3 ,

for example

1 2 3 .........{1+ 2 + 3 = 6}

34 5 ........ { 3 + 4 + 5 = 12}

2 0 4 .........{ 2 + 0 + 4 = 6}

5- If the last digit is 0 or 5 e.g. 50, 65, 70

11 - If the last sum of the alternate digit are equal

or their difference is a multiple of 11,

e.g

1 8 7 ...... ( 1 +7) - 8= 0

8 1 9 3 9....{8 + 9 + 9} -{1 +3} = 22

Hello

Have fun as you go through this lesson on Greatest Common Divisor or Highest Common Factor.

.

Greatest Common Divisor

## e-Content

Buy e-Content Digital CD covers all the topics for a particular class per year. One CDs costs 1200/-

click to play video

Purchase Online and have the CD sent to your nearest Parcel Service. Pay the amount to Patrick 0721806317 by M-PESA then provide your address for delivery of the Parcel.. Ask for clarification if in doubt,

Greatest Common Divisor

###### We have an enourmous data quiz bank of past papers ranging from 1995 - 2017

KCSE ONLINE WEBSITE provide KCSE, KCPE and MOCK Past Papers which play a great role in students� performance in the KCSE examination. KCSE mock past papers serves as a good motivation as well as revision material for the major exam the Kenya certificate of secondary education (KCSE). Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE . Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE. It is also cost effective

#### MOCK Past Papers

As a student, you will have access to the most important resources that can help you understand what is required for you to sit and pass your KCSE examination and proceed to secondary school or gain entry to University admission respectively.

#### KCSE ONLINE

Similar

More

Similar

KCSE ONLINE WEBSITE provide KCSE, KCPE and MOCK Past Papers which play a great role in students� performance in the KCSE examination.

Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE. It is also cost effective

Ask for clarification if in doubt, vitae dignissim est posuere id.

Greatest Common Divisor

sit amet congue Mock Past Papers, give you an actual exam situation in readiness for your forthcoming national examination from the Kenya National Examination Council KNEC

Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE. It is also cost effective sapien.

Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE. It is also cost effective sapien.

Greatest Common Divisor

As a supplementary to coursework content our e-library for digitized multimedia CDs while enhance and ensure that you never missed that important concept during the normal class lessons. It is a Do it Yourself Project..

Candidates who would want their papers remarked should request for the same within a month after release of the results. Those who will miss out on their results are advised to check with their respective school heads and not with the examination council

For Best results INSTALL Adobe Flash Player Version 16 to play the interactive content in your computer. Test the link below to find out if you have Adobe Flash in your computer.

### New Register

Similar

Buy e-Content Digital CD covering all the topics for a particular class per year. One CDs costs 1200/- ( Per Subject per Class )

### New Membership

Also

We have an enourmous data quiz bank of past papers ranging from 1995 - 2017

### Register

Gold

Register as gold member and get access to KCSE and KCPE resources for one year. subscription is 1000/- renewable yearly.