Join Our Email Alerts-Subscribe
Important Note:Login & Check Your Email Inbox and Activate Confirmation Link


Enter Your Email :

Copyright Disclaimer:
Section 107 of the Copyright Act Fair Use Contents .
We are forwarding content link(s) from our website to content website & We are not serving any contents.
Main Source:Google.com.All the Content PDF link(s) is/are obtained from GoogleSearch
for the purpose of Education & Teaching Intention. Not for commercial purpose.
Technicalsymposium.com is not liable/responsible for any copyright issues.

Highest Common Factor (H.C.F.) or Greatest Common Measure (G.C.M.) or Greatest Common Divisor (G.C.D.)

There are two methods of finding the H.C.F. of a given set of numbers:

1. Factorization Method

2. Division method

1. Factorization Method: Express the each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives H.C.F.

2. Division Method: Suppose we have to find the H.C.F. of two given numbers, divide the larger by the smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is required H.C.F.

Finding the H.C.F. of more than two numbers: Suppose we have to find the H.C.F. of three numbers, then, H.C.F. of [(H.C.F. of any two) and (the third number)] gives the H.C.F. of three given number.

Similarly, the H.C.F. of more than three numbers may be obtained.

Least Common Multiple (L.C.M.)

The least number which is exactly divisible by each one of the given numbers is called their L.C.M.

There are two methods of finding the L.C.M. of a given set of numbers:

1. Factorization Method,

2. Division Method (Division Method is short cut method of LCM)

1. Factorization Method: Resolve each one of the given numbers into a product of prime factors. Then, L.C.M. is the product of highest powers of all the factors.

2. Division Method : Arrange the given numbers in a row in any order. Divide by a number which divided exactly at least two of the given numbers and carry forward the numbers which are not divisible. Repeat the above process till no two of the numbers are divisible by the same number except 1. The product of the divisors and the undivided numbers is the required L.C.M. of the given numbers.

Factors and Multiples

if number a divided another number b exactly, we say that a is a factor of b. In this case, b is called a multiple of a.

6. HCF and LCM of Fractions

When solving HCF and LCM questions with fractions these formulas are very helpful

1. H.C.F. = H.C.F. of NumeratorsL.C.M. of Denominators2. L.C.M. = L.C.M. of NumeratorsH.C.F. of Denominators

Problems on Numbers Formulae

1. (a + b)(a - b) = (a2 - b2)

2. (a + b)2 = (a2 + b2 + 2ab)

3. (a - b)2 = (a2 + b2 - 2ab)

4. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

5. (a3 + b3) = (a + b)(a2 - ab + b2)

6. (a3 - b3) = (a - b)(a2 + ab + b2)

7. (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)

8. When a + b + c = 0, then a3 + b3 + c3 = 3abc.

Source: Contents are provided by Technicalsymposium.com Google Group Members.

Disclaimer: All the above contents are provided by technicalsymposium.com Google Group members.

Further, this content is not intended to be used for commercial purpose.

Technicalsymposium.com is not liable/responsible for any copyright issues.


Copyright Disclaimer:Section 107 of the Copyright Act Fair Use Contents .
We are forwarding content link(s) from our website to content website & We are not serving any contents. Main Source:Google.com.All the Content PDF link(s) is/are obtained from GoogleSearch for the purpose of Education & Teaching Intention. Not for commercial purpose. Technicalsymposium.com is not liable/responsible for any copyright issues.

Fresher Jobs & IT Jobs and Off-Campus

Programming & Projects PDF

Conferences & Symposium Details

B.E/Medical Lecture Notes PDF

GRE/TOEFL/IELTS/GMAT/SAT Notes

Aptitude/Placement Papers

Technicalsymposium.com-Contents

Technicalsymposium.com-Contents

Conference & Symposium Details

Government Jobs Details

Off-Campus Interviews & Walk-in/Career Pages

Software Jobs and IT Jobs Details

Bank Jobs & PO/Clerk Jobs Preparation Books PDF

Bank Quick Study Notes & Question Papers PDF

IES Syllabus & Question Papers-Free Download

Placement Papers with Answers PDF

Aptitude Study Notes & Puzzles PDF

Technical Interview Questions with Answers PDF





Technicalsymposium.com-Contents

Technicalsymposium.com-Contents

BE/B.Tech/M.Sc & B.Sc & Commerce Lecture Notes-Free Download

Engineering Maths Lecture Notes-Free Download

GRE Study Materials & Notes-Free Download

TOEFL Study Materials-Free Download.

IELTS Study Materials & ebooks-Free Download

GMAT Study Materials-Free Download

SAT Study Materials & ebooks-Free Download

Engineering Physics Lecture Notes-Free Download





Technicalsymposium.com-Contents

Technicalsymposium.com-Contents

Resume Formats and Resume Writing Tips

Group Discussion Topics & Answers

HR & Situational and Behavioral Interview Questions & Answers

General Job Interviews Materials-Free Download

Engineering Chemistry Lecture Notes-Free Download

Anna University Question Papers and Study Notes PDF

Programming & Manuals and Projects PDF

GATE Question Papers and Study Materials & ebooks PDF

All Engineering ebooks & Study Notes PDF

Paper Abstracts and Conference Papers PDF