Question

Find the hcf of 144 and 89 by Euclid's Division Lemma Method. ​

Answer 1

Answer:

• The divisor at this stage, ie, 1 is the HCF 144 and 89.

Given :

• The numbers 144 and 89.

To find :

• HCF of 144 and 89 by Euclid method =?

Step-by-step explanation:

Clearly, 144 > 89

Applying the Euclid's division lemma to 144 and 89, we get

144 = 89 x 1 + 55

Since the remainder 55 ≠ 0, we apply the Euclid's division lemma to divisor 89 and remainder 55 to get

89 = 55 x 1 + 34

We consider the new divisor 55 and remainder 34 and apply the division lemma to get

55 = 34 x 1 + 21

We consider the new divisor 34 and remainder 21 and apply the division lemma to get

34 = 21 x 1 + 13

We consider the new divisor 21 and remainder 13 and apply the division lemma to get

21 = 13 x 1 + 8

We consider the new divisor 13 and remainder 8 and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and remainder 5 and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and remainder 3 and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and remainder 2 and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and remainder 1 and apply the division lemma to get

2 = 1 x 1 + 1

We consider the new divisor 36 and remainder 13 and apply the division lemma to get

1 = 1 x 1 + 0

Now, the remainder at this stage is 0.

So, the divisor at this stage, ie, 1 is the HCF of 144 and 89.