Question

Use Euclid's division algorithm to find the \[HCF\]of $135$ and $225$.

Answer 1

Hint:-Here, we divide $225$ by $135$. If remainder does not come to zero. Then again divide the divisor by the remainder. Repeat this step until the remainder becomes zero.

Given numbers$135$ and $225$
Here, $225 > 135$
 So, we will divide greater number by smaller number
The quotient is $1$ and remainder is $90$.
$225 = 135 \times 1 + 90$
Now we have to divide the divisor by the remainder
Divide $135$ by $90$
The quotient is $1$ and remainder is $45$
$135 = 90 \times 1 + 45$
We have to repeat the above step until we get the remainder zero
Divide $90$ by $45$
The quotient is $2$ and remainder is $0$.
$90 = 2 \times 45 + 0$
Thus, the HCF is $45$
Note:- Whenever such types of questions are given to find \[HCF\], we have to first divide the larger number by a smaller number .If the remainder does not come to zero then again divide the divisor by the remainder. Repeat this step until the remainder becomes zero. When remainder becomes zero the last divisor is the required answer.