Question

Express the hcf of 18&24 in the form of 18m+24n, then find the value of m&n.

Answer 1

By Euclid's division algorithm,
24=18×1+6
18=6×3+0
HCF of 24,18=6
6=24×1-18×1
6=24×1+18×(-1)
on comparing
m=-1,n=1

Answer 2

Answer: $m=-1\ and\ n=1$

Step-by-step explanation:

Given: $HCF(18,24)=18m+24n$

The factors of $18=1,2,3,6,9,18$

The factors of $24=1,2,3,4,6,8,12,24$

The highest common factor of 18 and 24 can be written as :-

$HCF=6$

We can write 6 in the form of 24 and 18 as :

$6=24-18$

When we compare to the given form we get

$m=-1\ and\ n=1$