The HCF of135 and 225 by using Euclid’s division algorithm is ____.

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Detailed Solution

We are asked to find the HCFs of 135 and 225 using the Euclidean division.
Now let's apply the first step, i.e. divide the number 225 by 135, then we get
⇒225 = (135×1) + 90
Here we see that the divisor used in the previous division is 135 and the remainder is 90
Now let's apply the second step, i.e. divide the number 135 by 90, then we get
⇒135 = (90×1) + 45
Here we see that the divisor used in the previous division is 90 and the remainder is 45
Now let's apply the second step, i.e. divide the number 90 by 45, then we get
⇒90 = (45×2) + 0
Here we see that we got the remainder in the previous division as 0 when the divisor is 45
Now we use the fourth step which 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

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