Question

If H.C.F. of 210 and 55 is expressed in the form of 210 $\times$ 5 + 55y, find the value of $y^2$.

• A. $381$
• B. $368$
• C. $361$
• D. $19$

Answer 1

Answer: (C)

$361$

factors of $210=1\times 2\times 3\times 5\times 7$

factors of $55=1\times 5\times 11$

common factors = 1, 5

HCF $=1\times 5=5$

Therefore, according to equation,

$5=210\times 5+55y$

Dividing by 5,

$1=210+11y$

$1-210=11y-209=11y\frac{-209}{11}=yy=(-19)$

And,

$y^2=(-19)(-19)y^2=361$