Question

Using Euclid's division algorithm,find the HCF of 75 and 160.

Answer 1

Answer:

Step-by-step explanation:

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

Answer:

5 is the hcf of 75 and 160

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