Question

using Euclid's division algorithm find the HCF of 75and160​

Answer 1

Given :

• 160 and 75

To find :

• H. C. F by using Euclid's Division Algorithm =?

Step-by-step explanation :

Euclid's division lemma :

Let a and b be any two positive Integers .

Then there exist two unique whole numbers q and r such that

a = bq + r ,

0 ≤ r <b

Now ,

Start with a larger integer , that is 160,

Applying the Euclid's division lemma to 160 and 75, we get

160 = 75 × 2 + 10

Since the remainder 10 ≠ 0, we apply the Euclid's division lemma to divisor 75 and remainder 10 to get

75 = 10 × 7 + 5

We consider the new divisor 10 and remainder 5 and apply the division lemma to get

10 = 5 × 2 + 0

Now, the remainder at this stage is 0.

So, the divisor at this stage, ie, 5 is the HCF of 160 and 75.

Answer 2

$\huge\underline\mathrm{GivEn:-}$

⭐ 75 and 160

$\huge\underline\mathrm{To\: Find:-}$

⭐ HCF by using Euclid's algorithm

$\huge\underline\mathrm{SoLution:-}$

Given integers are 75 and 160 such that 160>75. Applying Euclid's division lemma to 160 and 75, we get

$\implies$ 160 = 75 x 2 + 10

Since the remainder 10 is not equal to 0. so we applying Euclid's division lemma to 75 and 10, to get

$\implies$ 75 = 10 x 7 + 5

We consider the new divisor 10 and new remainder 5 and apply division lemma to get

$\implies$ 10 = 5 x 2 + 0

We observe that the remainder at this stage is zero. Therefore, the divisor at this stage i.e., 5(or the remainder at the earlier stage) is the HCF of 160 and 75.

$\huge\underline\mathrm{ThAnKs...}$