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.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The radius of the base and the height of a solid right circular cylinder are in the ratio $2 : 3$ and its volume is $1617\ cm^3$. Find the total surface area of the cylinder. $\Big[\text{Take}\ \pi=\frac{22}{7}.\Big]$
→Evaluate:
$=\tan7^\circ\tan23^\circ\tan60^\circ\tan67^\circ\tan83^\circ$
→$=\tan7^\circ\tan23^\circ\tan60^\circ\tan67^\circ\tan83^\circ$
On which axis do the following points lie?
Q(0, -2).
Q(0, -2).
Write the discriminant of the following quadratic equation.
$x^2 + 2x + 4 = 0$
→$x^2 + 2x + 4 = 0$
Find the fourth term from the end in an A.P. – 11, – 8, – 5, . . ., 49.
In the given pairs of triangles, find which pair of triangles are similar. State the similarity criterior and write the similarity relation in symbolic from.
The radii of two circular ends of frustum shape bucket are 14 cm and 7 cm. Height of the bucket is 30 cm. How many liters of water it can hold? (1 litre = $1000 \mathrm{~cm}^3$)
→In the equation 2𝑥 − 𝑦 = 2 if 𝑥 = 3 then find y=?
The given sequence is AP or not ? If they are A.P. find the common difference.
$0, – 4, – 8, – 12, . . .$
→$0, – 4, – 8, – 12, . . .$
The area of a sector of a circle of radius 2cm is $\pi\text{cm}^2.$ Find the angle contained by the sector.
→