Question

find the HCF of 135 and 225 by Euclid's Divivsion Lemma

Answer 1

Answer:

Step-by-step explanation:

We are asked to find the HCF of 135 and 225 using Euclid’s division.

We know that the steps involved in Euclid’s division are

(1) We divide the large number with a small number and take the remainder.

(2) Next we divide the divisor used in the previous division with the remainder we got in the previous division and take the remainder.

(3) We carry out step (2) until we get the remainder as 0.

(4) The divisor used when the remainder is 0 will be the HCF of the given two numbers.

Now, let us apply the first step that is let us divide the number 225 with 135 then we get

⇒225=(135×1)+90

Here we can see that the divisor used in the previous division is 135 and the remainder is 90

Now, let us apply the second step that is let us divide the number 135 with 90 then we get

⇒135=(90×1)+45

Here we can see that the divisor used in the previous division is 90 and the remainder is 45

Now, let us apply the second step that is let us divide the number 90 with 45 then we get

⇒90=(45×2)+0

Here we can see that we got the remainder in the previous division as 0 when the divisor is 45

Now, let us apply the fourth step that is the divisor used to get the remainder 0 is the HCF

Therefore we can conclude that the HCF of 135 and 225 is 45

∴HCF(135,225)=45