Question

The quickest way of finding out HCF in Mathematics ?

Answer 1

Euclid 's algorithm is the fastest way to find HCF , which is very effective even for large numbers , rather than the usual factorization with writing out common factors .

As an example , here is the usual method

HCF (280 ; 320 ) = ?

We decompose 320 and 280 into prime factors

`\begin{array}r 320 & 2 \\ 160 &2 \\ 80 & 2 \\ 40 &2 \\ 20 &2 \\ 10 & 2 \\ 5 & 5 \end{array}`

280 = 2·2·2·5·7

320 = 2·2·2·2·2·2·5

Thus HCF ( 280 ; 320 ) = 2·2·2·5 = 40

Euclid 's algorithm

HCF ( 280 ; 320 ) = 40

We divide the divisor by the remainder until zero remains in the remainder