Question
Use Euclid's division algorithm to find the $HCF$ of:
$135$ and $225$
$135$ and $225$
✓
Answer
We have $225 > 135,$
So, we apply the division lemma to $225$ and $135$ to obtain.
$225 = 135 × 1 + 90$
Here remainder $90 ≠ 0,$ we apply the division lemma again to $135$ and $90$ to obtain.
$135 = 90 × 1 + 45$
We consider the new divisor $90$ and new remainder $45 ≠ 0,$ and apply the division lemma to obtain.
$90 = 2 × 45 + 0$
Since at this time the remainder is zero, the process is stopped.
The divisor at this stage is $45$
Therefore, the $HCF$ of $135$ and $225$ is $45.$
So, we apply the division lemma to $225$ and $135$ to obtain.
$225 = 135 × 1 + 90$
Here remainder $90 ≠ 0,$ we apply the division lemma again to $135$ and $90$ to obtain.
$135 = 90 × 1 + 45$
We consider the new divisor $90$ and new remainder $45 ≠ 0,$ and apply the division lemma to obtain.
$90 = 2 × 45 + 0$
Since at this time the remainder is zero, the process is stopped.
The divisor at this stage is $45$
Therefore, the $HCF$ of $135$ and $225$ is $45.$
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