# Real Numbers

## Class 10 NCERT

### NCERT

1   Use Euclid’s division algorithm to find the HCF of : $\\$ (i) $135$ and $225$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ (ii) $196$ and $38220$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ (iii) $867$ and $255$

##### Solution :

$\textbf{(i)$135$and$225$}$ $\\$ Since $225 > 135$, we apply the division lemma to $225$ and $135$ to obtain $\\$ $225 = 135 \times 1 + 90$ $\\$ Since remainder $90\ \ne 0$, we apply the division lemma to $135$ and $90$ to obtain $\\$ $135 = 90 \times 1 + 45$ $\\$ We consider the new divisor $90$ and new remainder $45,$ and apply the division lemma to obtain $\\$ $90 = 2 \times 45 + 0$ $\\$ Since the remainder is zero, the process stops. $\\$ Since the divisor at this stage is $45$, $\\$ Therefore, the $HCF$ of $135$ and $225$ is $45.$ $\\$