E-Maths: Application of Highest Common Factor (HCF) Concept

Many students upon reading this question might not realise that it is testing our understanding of the concept on Highest Common Factor learnt in Secondary 1 Mathematics.

A floor 6.8m width and 11.05m length is to be paved with equal square tiles. Find the number of largest dimension square tiles that exactly fit the floor?

Step 1: I converted the metres into centimetres by multiplying with 100 (1m = 100cm) so that I can work with whole numbers instead of decimals.

6.8m = 680cm
11.05m = 1105cm

Step 2: I express each dimension in index notation by prime factorisation method.

$680=2^{3}\times&space;5\times&space;17$

$1105&space;=&space;5\times&space;13\times&space;17$

Step 3: I find the HCF of these two numbers

HCF $=5&space;\times&space;17=85cm=0.85m$

This means the largest dimension of square tile will be 0.85m by 0.85m

Number of largest dimension square tiles used

$=\frac{6.8}{0.85}\times\frac{11.05}{0.85}$

$=104$

Question of similar nature was asked in the recent year GCE O-Level examination in Paper 1 and many students did not know how to approach the question. I hope you find the explanation clear. It is always recommended to sketch a simple diagram to get your thinking started.

Ai Ling Ong

Hi, I'm Ai Ling Ong. I enjoy coaching students who have challenges with understanding and scoring in 'O' Level A-Maths and E-Maths. I develop Math strategies, sometimes ridiculous ideas to help students in understanding abstract concepts the fast and memorable way. I write this blog to share with you the stuff I teach in my class, the common mistakes my students made, the 'way' to think, analyze... If you have found this blog post useful, please share it with your friends. I will really appreciate it! :)