Question

use euclid's division algorithm to find hcf of 870 and 225

Answer 1

The HCF of 870 and 225 is 15

Step-by-step explanation:

Euclids division algorithm: If there are two positive integers a, b there exists q and r which satisfies a = bq + r where 0 < r ≤ b

It is a technique used to find the highest common factor of two positive integers. HCF is the largest number that divides both the integers until the remainder is zero.

Out of the two given numbers, we consider the greater number first and then follow Euclids algorithm.

Now, here 870 is the greater number among the given numbers.

Hence, 15 is the HCF for 870 and 225.

Answer 2

Answer:

HCF of 870 and 225 is 15

Step-by-step explanation:

Euclid's Division Algorithm:

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

Here , a is called the dividend , b is called the divisor , q is called the quotient and r is called remainder.

Start with larger integer , that is 870.

Apply the division lemma to 870 and 225 ,to get

870 = 225×3+195

Since, the remainder is not equal to zero , we apply the division lemma to 225 and 195 to get

225 = 195 × 1 + 30

Apply again,

195 = 30 × 6 + 15

30 = 15 ×2 + 0

The remainder has now become zero, so our procedure stops .

Since the divisor at this stage is 15,the HCF of 870 and 225 is 15

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