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# Geometry/Highest Common Factor

Question
Hello sir

sir can you tell me why in factoristation , hcf of 2 and 4 is 2 , there shold 4 because it is highest common factor

Hi Shilpa,

Highest common factor, all three words are important.  The key one for this case is COMMON.

To find the highest common factor, you can do this.

1) List the factors of both numbers.
2) Compare the lists, keeping only the factors that appear in both (that is the common factors).
3) Select the highest of those numbers.

So in the case of 2 and 4:

1) 2 has factors (2); 4 has factors (2,4).
2) The only factor that appears in both lists is 2.
3) The highest number in the common list must be the only number 2.

The factors must be common.  Don't just look at the highest number.  It is actually impossible for the highest of the two original numbers to be the hcf.

Regards,
Azeem

Geometry

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#### Azeem Hussain

##### Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

##### Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

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CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.